3+20i-5i

Multiply the numerator and denominator of 3+20i-5i by the conjugate of -5i to make the denominator real.

3+20i-5i⋅ii

Combine.

(3+20i)i-5ii

Simplify the numerator.

Apply the distributive property.

3i+20ii-5ii

Multiply 20ii.

Raise i to the power of 1.

3i+20(i1i)-5ii

Raise i to the power of 1.

3i+20(i1i1)-5ii

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

3i+20i1+1-5ii

Add 1 and 1.

3i+20i2-5ii

3i+20i2-5ii

Simplify each term.

Rewrite i2 as -1.

3i+20⋅-1-5ii

Multiply 20 by -1.

3i-20-5ii

3i-20-5ii

Reorder 3i and -20.

-20+3i-5ii

-20+3i-5ii

Simplify the denominator.

Add parentheses.

-20+3i-5(ii)

Raise i to the power of 1.

-20+3i-5(i1i)

Raise i to the power of 1.

-20+3i-5(i1i1)

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

-20+3i-5i1+1

Add 1 and 1.

-20+3i-5i2

Rewrite i2 as -1.

-20+3i-5⋅-1

-20+3i-5⋅-1

-20+3i-5⋅-1

Multiply -5 by -1.

-20+3i5

Split the fraction -20+3i5 into two fractions.

-205+3i5

Divide -20 by 5.

-4+3i5

Rewrite in Standard Form (3+20i)/(-5i)