Question

Express the complex number in trigonometric form.

-5i

A) 5(cos 270° + i sin 270°)
B) 5(cos 180° + i sin 180°)
C) 5(cos 90° + i sin 90°)
D) 5(cos 0° + i sin 0°)

Answer 1

-5i can be written as 0 + (-5)i
It is in the form a+bi where a = 0 and b =-5
So the point (a,b) is (0,-5)

The distance from the origin to this point is 5 units, therefore r = 5. This is the magnitude.

The angle is 270 degrees as shown in the attached image. You start on the positive x axis and rotate until you reach the point (0,-5)

This is why the answer is choice A) 5(cos(270) + i*sin(270))