can you work out the problem as well

**Answer 1**

Let 5 – 5i = r(cos(t) + i sin(t))

Equating real and imaginary parts:

5 = r cos(t)

– 5 = r sin(t)

Squaring and adding:

25 + 25 = r^2

r = sqrt(50)

= 5 sqrt(2).

cos(t) = 5 / r = 1 / sqrt(2)

sin(t) = – 5 / r = – 1 / sqrt(2)

t is a quadrant 4 angle.

t = 2pi – pi / 4 = 7pi / 4.

5 – 5i = 5 sqrt(2) [ cos(7pi / 4) + i sin(7pi / 4) ].