Graph (1- square root of 3i)^7

Math
(1-3i)7
Use the Binomial Theorem.
y=17+7⋅16(-3i)+21⋅15(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Simplify terms.
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Simplify each term.
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One to any power is one.
y=1+7⋅16(-3i)+21⋅15(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
One to any power is one.
y=1+7⋅1(-3i)+21⋅15(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 7 by 1.
y=1+7(-3i)+21⋅15(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply -1 by 7.
y=1-7(3i)+21⋅15(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
One to any power is one.
y=1-73i+21⋅1(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 21 by 1.
y=1-73i+21(-3i)2+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -3i.
y=1-73i+21((-3)2i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Apply the product rule to -3.
y=1-73i+21((-1)232i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i+21((-1)232i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Raise -1 to the power of 2.
y=1-73i+21(132i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 32 by 1.
y=1-73i+21(32i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite 32 as 3.
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Use axn=axn to rewrite 3 as 312.
y=1-73i+21((312)2i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Apply the power rule and multiply exponents, (am)n=amn.
y=1-73i+21(312⋅2i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Combine 12 and 2.
y=1-73i+21(322i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Cancel the common factor of 2.
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Cancel the common factor.
y=1-73i+21(322i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Divide 1 by 1.
y=1-73i+21(31i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i+21(31i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Evaluate the exponent.
y=1-73i+21(3i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i+21(3i2)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite i2 as -1.
y=1-73i+21(3⋅-1)+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 3 by -1.
y=1-73i+21⋅-3+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 21 by -3.
y=1-73i-63+35⋅14(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
One to any power is one.
y=1-73i-63+35⋅1(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 35 by 1.
y=1-73i-63+35(-3i)3+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -3i.
y=1-73i-63+35((-3)3i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Apply the product rule to -3.
y=1-73i-63+35((-1)333i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+35((-1)333i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Raise -1 to the power of 3.
y=1-73i-63+35(-33i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite 33 as (33)12.
y=1-73i-63+35(-33i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Raise 3 to the power of 3.
y=1-73i-63+35(-27i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite 27 as 32⋅3.
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Factor 9 out of 27.
y=1-73i-63+35(-9(3)i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite 9 as 32.
y=1-73i-63+35(-32⋅3i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+35(-32⋅3i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Pull terms out from under the radical.
y=1-73i-63+35(-(33)i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 3 by -1.
y=1-73i-63+35(-33i3)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Factor out i2.
y=1-73i-63+35(-33(i2⋅i))+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite i2 as -1.
y=1-73i-63+35(-33(-1⋅i))+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite -1i as -i.
y=1-73i-63+35(-33(-i))+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply -1 by -3.
y=1-73i-63+35(33i)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 3 by 35.
y=1-73i-63+105(3i)+35⋅13(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
One to any power is one.
y=1-73i-63+1053i+35⋅1(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 35 by 1.
y=1-73i-63+1053i+35(-3i)4+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -3i.
y=1-73i-63+1053i+35((-3)4i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Apply the product rule to -3.
y=1-73i-63+1053i+35((-1)434i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+35((-1)434i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Raise -1 to the power of 4.
y=1-73i-63+1053i+35(134i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 34 by 1.
y=1-73i-63+1053i+35(34i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite 34 as 32.
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Use axn=axn to rewrite 3 as 312.
y=1-73i-63+1053i+35((312)4i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Apply the power rule and multiply exponents, (am)n=amn.
y=1-73i-63+1053i+35(312⋅4i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Combine 12 and 4.
y=1-73i-63+1053i+35(342i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Cancel the common factor of 4 and 2.
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Factor 2 out of 4.
y=1-73i-63+1053i+35(32⋅22i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Cancel the common factors.
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Factor 2 out of 2.
y=1-73i-63+1053i+35(32⋅22(1)i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Cancel the common factor.
y=1-73i-63+1053i+35(32⋅22⋅1i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite the expression.
y=1-73i-63+1053i+35(321i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Divide 2 by 1.
y=1-73i-63+1053i+35(32i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+35(32i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+35(32i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+35(32i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Raise 3 to the power of 2.
y=1-73i-63+1053i+35(9i4)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite i4 as 1.
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Rewrite i4 as (i2)2.
y=1-73i-63+1053i+35(9(i2)2)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Rewrite i2 as -1.
y=1-73i-63+1053i+35(9(-1)2)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Raise -1 to the power of 2.
y=1-73i-63+1053i+35(9⋅1)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+35(9⋅1)+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 9 by 1.
y=1-73i-63+1053i+35⋅9+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 35 by 9.
y=1-73i-63+1053i+315+21⋅12(-3i)5+7⋅1(-3i)6+(-3i)7
One to any power is one.
y=1-73i-63+1053i+315+21⋅1(-3i)5+7⋅1(-3i)6+(-3i)7
Multiply 21 by 1.
y=1-73i-63+1053i+315+21(-3i)5+7⋅1(-3i)6+(-3i)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -3i.
y=1-73i-63+1053i+315+21((-3)5i5)+7⋅1(-3i)6+(-3i)7
Apply the product rule to -3.
y=1-73i-63+1053i+315+21((-1)535i5)+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+315+21((-1)535i5)+7⋅1(-3i)6+(-3i)7
Raise -1 to the power of 5.
y=1-73i-63+1053i+315+21(-35i5)+7⋅1(-3i)6+(-3i)7
Rewrite 35 as (35)12.
y=1-73i-63+1053i+315+21(-35i5)+7⋅1(-3i)6+(-3i)7
Raise 3 to the power of 5.
y=1-73i-63+1053i+315+21(-243i5)+7⋅1(-3i)6+(-3i)7
Rewrite 243 as 92⋅3.
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Factor 81 out of 243.
y=1-73i-63+1053i+315+21(-81(3)i5)+7⋅1(-3i)6+(-3i)7
Rewrite 81 as 92.
y=1-73i-63+1053i+315+21(-92⋅3i5)+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+315+21(-92⋅3i5)+7⋅1(-3i)6+(-3i)7
Pull terms out from under the radical.
y=1-73i-63+1053i+315+21(-(93)i5)+7⋅1(-3i)6+(-3i)7
Multiply 9 by -1.
y=1-73i-63+1053i+315+21(-93i5)+7⋅1(-3i)6+(-3i)7
Factor out i4.
y=1-73i-63+1053i+315+21(-93(i4i))+7⋅1(-3i)6+(-3i)7
Rewrite i4 as 1.
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Rewrite i4 as (i2)2.
y=1-73i-63+1053i+315+21(-93((i2)2i))+7⋅1(-3i)6+(-3i)7
Rewrite i2 as -1.
y=1-73i-63+1053i+315+21(-93((-1)2i))+7⋅1(-3i)6+(-3i)7
Raise -1 to the power of 2.
y=1-73i-63+1053i+315+21(-93(1i))+7⋅1(-3i)6+(-3i)7
y=1-73i-63+1053i+315+21(-93(1i))+7⋅1(-3i)6+(-3i)7
Multiply i by 1.
y=1-73i-63+1053i+315+21(-93i)+7⋅1(-3i)6+(-3i)7
Multiply -9 by 21.
y=1-73i-63+1053i+315-189(3i)+7⋅1(-3i)6+(-3i)7
Multiply 7 by 1.
y=1-73i-63+1053i+315-1893i+7(-3i)6+(-3i)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -3i.
y=1-73i-63+1053i+315-1893i+7((-3)6i6)+(-3i)7
Apply the product rule to -3.
y=1-73i-63+1053i+315-1893i+7((-1)636i6)+(-3i)7
y=1-73i-63+1053i+315-1893i+7((-1)636i6)+(-3i)7
Raise -1 to the power of 6.
y=1-73i-63+1053i+315-1893i+7(136i6)+(-3i)7
Multiply 36 by 1.
y=1-73i-63+1053i+315-1893i+7(36i6)+(-3i)7
Rewrite 36 as 33.
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Use axn=axn to rewrite 3 as 312.
y=1-73i-63+1053i+315-1893i+7((312)6i6)+(-3i)7
Apply the power rule and multiply exponents, (am)n=amn.
y=1-73i-63+1053i+315-1893i+7(312⋅6i6)+(-3i)7
Combine 12 and 6.
y=1-73i-63+1053i+315-1893i+7(362i6)+(-3i)7
Cancel the common factor of 6 and 2.
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Factor 2 out of 6.
y=1-73i-63+1053i+315-1893i+7(32⋅32i6)+(-3i)7
Cancel the common factors.
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Factor 2 out of 2.
y=1-73i-63+1053i+315-1893i+7(32⋅32(1)i6)+(-3i)7
Cancel the common factor.
y=1-73i-63+1053i+315-1893i+7(32⋅32⋅1i6)+(-3i)7
Rewrite the expression.
y=1-73i-63+1053i+315-1893i+7(331i6)+(-3i)7
Divide 3 by 1.
y=1-73i-63+1053i+315-1893i+7(33i6)+(-3i)7
y=1-73i-63+1053i+315-1893i+7(33i6)+(-3i)7
y=1-73i-63+1053i+315-1893i+7(33i6)+(-3i)7
y=1-73i-63+1053i+315-1893i+7(33i6)+(-3i)7
Raise 3 to the power of 3.
y=1-73i-63+1053i+315-1893i+7(27i6)+(-3i)7
Factor out i4.
y=1-73i-63+1053i+315-1893i+7(27(i4i2))+(-3i)7
Rewrite i4 as 1.
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Rewrite i4 as (i2)2.
y=1-73i-63+1053i+315-1893i+7(27((i2)2i2))+(-3i)7
Rewrite i2 as -1.
y=1-73i-63+1053i+315-1893i+7(27((-1)2i2))+(-3i)7
Raise -1 to the power of 2.
y=1-73i-63+1053i+315-1893i+7(27(1i2))+(-3i)7
y=1-73i-63+1053i+315-1893i+7(27(1i2))+(-3i)7
Multiply i2 by 1.
y=1-73i-63+1053i+315-1893i+7(27i2)+(-3i)7
Rewrite i2 as -1.
y=1-73i-63+1053i+315-1893i+7(27⋅-1)+(-3i)7
Multiply 27 by -1.
y=1-73i-63+1053i+315-1893i+7⋅-27+(-3i)7
Multiply 7 by -27.
y=1-73i-63+1053i+315-1893i-189+(-3i)7
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -3i.
y=1-73i-63+1053i+315-1893i-189+(-3)7i7
Apply the product rule to -3.
y=1-73i-63+1053i+315-1893i-189+(-1)737i7
y=1-73i-63+1053i+315-1893i-189+(-1)737i7
Raise -1 to the power of 7.
y=1-73i-63+1053i+315-1893i-189-37i7
Rewrite 37 as (37)12.
y=1-73i-63+1053i+315-1893i-189-37i7
Raise 3 to the power of 7.
y=1-73i-63+1053i+315-1893i-189-2187i7
Rewrite 2187 as 272⋅3.
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Factor 729 out of 2187.
y=1-73i-63+1053i+315-1893i-189-729(3)i7
Rewrite 729 as 272.
y=1-73i-63+1053i+315-1893i-189-272⋅3i7
y=1-73i-63+1053i+315-1893i-189-272⋅3i7
Pull terms out from under the radical.
y=1-73i-63+1053i+315-1893i-189-(273)i7
Multiply 27 by -1.
y=1-73i-63+1053i+315-1893i-189-273i7
Rewrite i7 as i4(i2⋅i).
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Factor out i4.
y=1-73i-63+1053i+315-1893i-189-273(i4i3)
Factor out i2.
y=1-73i-63+1053i+315-1893i-189-273(i4(i2⋅i))
y=1-73i-63+1053i+315-1893i-189-273(i4(i2⋅i))
Rewrite i4 as 1.
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Rewrite i4 as (i2)2.
y=1-73i-63+1053i+315-1893i-189-273((i2)2(i2⋅i))
Rewrite i2 as -1.
y=1-73i-63+1053i+315-1893i-189-273((-1)2(i2⋅i))
Raise -1 to the power of 2.
y=1-73i-63+1053i+315-1893i-189-273(1(i2⋅i))
y=1-73i-63+1053i+315-1893i-189-273(1(i2⋅i))
Multiply i2⋅i by 1.
y=1-73i-63+1053i+315-1893i-189-273(i2⋅i)
Rewrite i2 as -1.
y=1-73i-63+1053i+315-1893i-189-273(-1⋅i)
Rewrite -1i as -i.
y=1-73i-63+1053i+315-1893i-189-273(-i)
Multiply -1 by -27.
y=1-73i-63+1053i+315-1893i-189+273i
y=1-73i-63+1053i+315-1893i-189+273i
Simplify by adding terms.
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Subtract 63 from 1.
y=-73i-62+1053i+315-1893i-189+273i
Add -73i and 1053i.
y=983i-62+315-1893i-189+273i
Subtract 1893i from 983i.
y=-913i-62+315-189+273i
Add -913i and 273i.
y=-643i-62+315-189
Simplify the expression.
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Add -62 and 315.
y=-643i+253-189
Subtract 189 from 253.
y=-643i+64
Reorder -643i and 64.
y=64-643i
y=64-643i
y=64-643i
y=64-643i
Graph (1- square root of 3i)^7

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