# Rewrite in Standard Form (3+3i)/(7-6i) 3+3i7-6i
Multiply the numerator and denominator of 3+3i7-6i by the conjugate of 7-6i to make the denominator real.
3+3i7-6i⋅7+6i7+6i
Multiply.
Combine.
(3+3i)(7+6i)(7-6i)(7+6i)
Simplify the numerator.
Expand (3+3i)(7+6i) using the FOIL Method.
Apply the distributive property.
3(7+6i)+3i(7+6i)(7-6i)(7+6i)
Apply the distributive property.
3⋅7+3(6i)+3i(7+6i)(7-6i)(7+6i)
Apply the distributive property.
3⋅7+3(6i)+3i⋅7+3i(6i)(7-6i)(7+6i)
3⋅7+3(6i)+3i⋅7+3i(6i)(7-6i)(7+6i)
Simplify and combine like terms.
Simplify each term.
Multiply 3 by 7.
21+3(6i)+3i⋅7+3i(6i)(7-6i)(7+6i)
Multiply 6 by 3.
21+18i+3i⋅7+3i(6i)(7-6i)(7+6i)
Multiply 7 by 3.
21+18i+21i+3i(6i)(7-6i)(7+6i)
Multiply 3i(6i).
Multiply 6 by 3.
21+18i+21i+18ii(7-6i)(7+6i)
Raise i to the power of 1.
21+18i+21i+18(i1i)(7-6i)(7+6i)
Raise i to the power of 1.
21+18i+21i+18(i1i1)(7-6i)(7+6i)
Use the power rule aman=am+n to combine exponents.
21+18i+21i+18i1+1(7-6i)(7+6i)
Add 1 and 1.
21+18i+21i+18i2(7-6i)(7+6i)
21+18i+21i+18i2(7-6i)(7+6i)
Rewrite i2 as -1.
21+18i+21i+18⋅-1(7-6i)(7+6i)
Multiply 18 by -1.
21+18i+21i-18(7-6i)(7+6i)
21+18i+21i-18(7-6i)(7+6i)
Subtract 18 from 21.
3+18i+21i(7-6i)(7+6i)
Add 18i and 21i.
3+39i(7-6i)(7+6i)
3+39i(7-6i)(7+6i)
3+39i(7-6i)(7+6i)
Simplify the denominator.
Expand (7-6i)(7+6i) using the FOIL Method.
Apply the distributive property.
3+39i7(7+6i)-6i(7+6i)
Apply the distributive property.
3+39i7⋅7+7(6i)-6i(7+6i)
Apply the distributive property.
3+39i7⋅7+7(6i)-6i⋅7-6i(6i)
3+39i7⋅7+7(6i)-6i⋅7-6i(6i)
Simplify.
Multiply 7 by 7.
3+39i49+7(6i)-6i⋅7-6i(6i)
Multiply 6 by 7.
3+39i49+42i-6i⋅7-6i(6i)
Multiply 7 by -6.
3+39i49+42i-42i-6i(6i)
Multiply 6 by -6.
3+39i49+42i-42i-36ii
Raise i to the power of 1.
3+39i49+42i-42i-36(i1i)
Raise i to the power of 1.
3+39i49+42i-42i-36(i1i1)
Use the power rule aman=am+n to combine exponents.
3+39i49+42i-42i-36i1+1
Add 1 and 1.
3+39i49+42i-42i-36i2
Subtract 42i from 42i.
3+39i49+0-36i2
Add 49 and 0.
3+39i49-36i2
3+39i49-36i2
Simplify each term.
Rewrite i2 as -1.
3+39i49-36⋅-1
Multiply -36 by -1.
3+39i49+36
3+39i49+36
Add 49 and 36.
3+39i85
3+39i85
3+39i85
Split the fraction 3+39i85 into two fractions.
385+39i85
Rewrite in Standard Form (3+3i)/(7-6i)

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