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

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)