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)

Add 15 and 4.

19+6i-10i(5-2i)(5+2i)

Subtract 10i from 6i.

19-4i(5-2i)(5+2i)

19-4i(5-2i)(5+2i)

19-4i(5-2i)(5+2i)

Simplify the denominator.

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

Apply the distributive property.

19-4i5(5+2i)-2i(5+2i)

Apply the distributive property.

19-4i5⋅5+5(2i)-2i(5+2i)

Apply the distributive property.

19-4i5⋅5+5(2i)-2i⋅5-2i(2i)

19-4i5⋅5+5(2i)-2i⋅5-2i(2i)

Simplify.

Multiply 5 by 5.

19-4i25+5(2i)-2i⋅5-2i(2i)

Multiply 2 by 5.

19-4i25+10i-2i⋅5-2i(2i)

Multiply 5 by -2.

19-4i25+10i-10i-2i(2i)

Multiply 2 by -2.

19-4i25+10i-10i-4ii

Raise i to the power of 1.

19-4i25+10i-10i-4(i1i)

Raise i to the power of 1.

19-4i25+10i-10i-4(i1i1)

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

19-4i25+10i-10i-4i1+1

Add 1 and 1.

19-4i25+10i-10i-4i2

Subtract 10i from 10i.

19-4i25+0-4i2

Add 25 and 0.

19-4i25-4i2

19-4i25-4i2

Simplify each term.

Rewrite i2 as -1.

19-4i25-4⋅-1

Multiply -4 by -1.

19-4i25+4

19-4i25+4

Add 25 and 4.

19-4i29

19-4i29

19-4i29

Split the fraction 19-4i29 into two fractions.

1929+-4i29

Move the negative in front of the fraction.

1929-4i29

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