Simplify (9+6i)(5+8i)

Math
(9+6i)(5+8i)
Expand (9+6i)(5+8i) using the FOIL Method.
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Apply the distributive property.
9(5+8i)+6i(5+8i)
Apply the distributive property.
9⋅5+9(8i)+6i(5+8i)
Apply the distributive property.
9⋅5+9(8i)+6i⋅5+6i(8i)
9⋅5+9(8i)+6i⋅5+6i(8i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 9 by 5.
45+9(8i)+6i⋅5+6i(8i)
Multiply 8 by 9.
45+72i+6i⋅5+6i(8i)
Multiply 5 by 6.
45+72i+30i+6i(8i)
Multiply 6i(8i).
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Multiply 8 by 6.
45+72i+30i+48ii
Raise i to the power of 1.
45+72i+30i+48(i1i)
Raise i to the power of 1.
45+72i+30i+48(i1i1)
Use the power rule aman=am+n to combine exponents.
45+72i+30i+48i1+1
Add 1 and 1.
45+72i+30i+48i2
45+72i+30i+48i2
Rewrite i2 as -1.
45+72i+30i+48⋅-1
Multiply 48 by -1.
45+72i+30i-48
45+72i+30i-48
Subtract 48 from 45.
-3+72i+30i
Add 72i and 30i.
-3+102i
-3+102i
Simplify (9+6i)(5+8i)

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