Express the complex number in trigonometric form. 5-5i?

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) ].

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