3+2i5-2i

Multiply the numerator and denominator of 3+2i5-2i by the conjugate of 5-2i to make the denominator real.

3+2i5-2i⋅5+2i5+2i

Combine.

(3+2i)(5+2i)(5-2i)(5+2i)

Simplify the numerator.

Expand (3+2i)(5+2i) using the FOIL Method.

Apply the distributive property.

3(5+2i)+2i(5+2i)(5-2i)(5+2i)

Apply the distributive property.

3⋅5+3(2i)+2i(5+2i)(5-2i)(5+2i)

Apply the distributive property.

3⋅5+3(2i)+2i⋅5+2i(2i)(5-2i)(5+2i)

3⋅5+3(2i)+2i⋅5+2i(2i)(5-2i)(5+2i)

Simplify and combine like terms.

Simplify each term.

Multiply 3 by 5.

15+3(2i)+2i⋅5+2i(2i)(5-2i)(5+2i)

Multiply 2 by 3.

15+6i+2i⋅5+2i(2i)(5-2i)(5+2i)

Multiply 5 by 2.

15+6i+10i+2i(2i)(5-2i)(5+2i)

Multiply 2i(2i).

Multiply 2 by 2.

15+6i+10i+4ii(5-2i)(5+2i)

Raise i to the power of 1.

15+6i+10i+4(i1i)(5-2i)(5+2i)

Raise i to the power of 1.

15+6i+10i+4(i1i1)(5-2i)(5+2i)

Use the power rule aman=am+n to combine exponents.

15+6i+10i+4i1+1(5-2i)(5+2i)

Add 1 and 1.

15+6i+10i+4i2(5-2i)(5+2i)

15+6i+10i+4i2(5-2i)(5+2i)

Rewrite i2 as -1.

15+6i+10i+4⋅-1(5-2i)(5+2i)

Multiply 4 by -1.

15+6i+10i-4(5-2i)(5+2i)

15+6i+10i-4(5-2i)(5+2i)

Subtract 4 from 15.

11+6i+10i(5-2i)(5+2i)

Add 6i and 10i.

11+16i(5-2i)(5+2i)

11+16i(5-2i)(5+2i)

11+16i(5-2i)(5+2i)

Simplify the denominator.

Expand (5-2i)(5+2i) using the FOIL Method.

Apply the distributive property.

11+16i5(5+2i)-2i(5+2i)

Apply the distributive property.

11+16i5⋅5+5(2i)-2i(5+2i)

Apply the distributive property.

11+16i5⋅5+5(2i)-2i⋅5-2i(2i)

11+16i5⋅5+5(2i)-2i⋅5-2i(2i)

Simplify.

Multiply 5 by 5.

11+16i25+5(2i)-2i⋅5-2i(2i)

Multiply 2 by 5.

11+16i25+10i-2i⋅5-2i(2i)

Multiply 5 by -2.

11+16i25+10i-10i-2i(2i)

Multiply 2 by -2.

11+16i25+10i-10i-4ii

Raise i to the power of 1.

11+16i25+10i-10i-4(i1i)

Raise i to the power of 1.

11+16i25+10i-10i-4(i1i1)

Use the power rule aman=am+n to combine exponents.

11+16i25+10i-10i-4i1+1

Add 1 and 1.

11+16i25+10i-10i-4i2

Subtract 10i from 10i.

11+16i25+0-4i2

Add 25 and 0.

11+16i25-4i2

11+16i25-4i2

Simplify each term.

Rewrite i2 as -1.

11+16i25-4⋅-1

Multiply -4 by -1.

11+16i25+4

11+16i25+4

Add 25 and 4.

11+16i29

11+16i29

11+16i29

Split the fraction 11+16i29 into two fractions.

1129+16i29

Rewrite in Standard Form (3+2i)/(5-2i)