Find the product (-5 + 5i)(7 - 7i) using trigonometric forms. Leave the result in trigonometric form.

Question

Options:

a. 35(cos 135deg + isin 135deg)

b. 70(cos 45deg + isin 45deg)

c. 35(cos 90deg + isin 90deg)

d. 70(cos 135deg + isin 135deg)

e. 70(cos 90deg + isin 90deg)

Answer 1

Hello Sam!

Note that

(-5 + 5i) = 5*(-1 +i)

(7-7i) = 7*(1 - i)

Remember that:

e^iθ = cosθ + isenθ

-1 = e^iπ

i = e^iπ/2

This expression can be written as:

(-5 + 5i)(7 - 7i) = 35*(-1 +i)*(1 - i) = -35*(-1 +i)² = -35* (1 -2i -1) = 70i = 70*e^iπ/2