Let z 38 9i and w 4 3i Compute the following and express

Let

z = 38 + 9i

and

w = 4 3i.

Compute the following and express your answer in

a + bi

form.

Solution

z/w

=(38 + 9i)/(4-3i)

multiply and divide by 4 +3i

=((38 + 9i)(4+3i))/((4-3i)(4+3i))

=((38*4)+(9*4 +38*3)i + (9i*3i))/(4²-(3i)²)

=(152+150i -27)/(16-(-9))

=(125+150i)/(25)

=(125/25)+(150/25)i

=5 +6i