# Rewrite in Standard Form 4/(-3-6i) 4-3-6i
Multiply the numerator and denominator of 4-3-6i by the conjugate of -3-6i to make the denominator real.
4-3-6i⋅-3+6i-3+6i
Multiply.
Combine.
4(-3+6i)(-3-6i)(-3+6i)
Simplify the numerator.
Apply the distributive property.
4⋅-3+4(6i)(-3-6i)(-3+6i)
Multiply 4 by -3.
-12+4(6i)(-3-6i)(-3+6i)
Multiply 6 by 4.
-12+24i(-3-6i)(-3+6i)
-12+24i(-3-6i)(-3+6i)
Simplify the denominator.
Expand (-3-6i)(-3+6i) using the FOIL Method.
Apply the distributive property.
-12+24i-3(-3+6i)-6i(-3+6i)
Apply the distributive property.
-12+24i-3⋅-3-3(6i)-6i(-3+6i)
Apply the distributive property.
-12+24i-3⋅-3-3(6i)-6i⋅-3-6i(6i)
-12+24i-3⋅-3-3(6i)-6i⋅-3-6i(6i)
Simplify.
Multiply -3 by -3.
-12+24i9-3(6i)-6i⋅-3-6i(6i)
Multiply 6 by -3.
-12+24i9-18i-6i⋅-3-6i(6i)
Multiply -3 by -6.
-12+24i9-18i+18i-6i(6i)
Multiply 6 by -6.
-12+24i9-18i+18i-36ii
Raise i to the power of 1.
-12+24i9-18i+18i-36(i1i)
Raise i to the power of 1.
-12+24i9-18i+18i-36(i1i1)
Use the power rule aman=am+n to combine exponents.
-12+24i9-18i+18i-36i1+1
-12+24i9-18i+18i-36i2
-12+24i9+0-36i2
-12+24i9-36i2
-12+24i9-36i2
Simplify each term.
Rewrite i2 as -1.
-12+24i9-36⋅-1
Multiply -36 by -1.
-12+24i9+36
-12+24i9+36
-12+24i45
-12+24i45
-12+24i45
Cancel the common factor of -12+24i and 45.
Factor 3 out of -12.
3(-4)+24i45
Factor 3 out of 24i.
3(-4)+3(8i)45
Factor 3 out of 3(-4)+3(8i).
3(-4+8i)45
Cancel the common factors.
Factor 3 out of 45.
3(-4+8i)3⋅15
Cancel the common factor.
3(-4+8i)3⋅15
Rewrite the expression.
-4+8i15
-4+8i15
-4+8i15
Split the fraction -4+8i15 into two fractions.
-415+8i15
Move the negative in front of the fraction.
-415+8i15
Rewrite in Standard Form 4/(-3-6i)     