Question

Express the complex number in trigonometric form -5i

Answer 1

you need two numbers, \(r\) and \(\theta\)
\(r\) is the absolute value, i.e. the distance from \((0,0)\) which is pretty clearly 5

Answer 2

yeah

Answer 3

\(\theta\) is the angle, which is not unique, but as you can see form the picture you can use \(-\frac{\pi}{2}\) or \(\frac{3\pi}{2}\) whatever you choose

Answer 4

you then write is as
\[r\left(\cos(\theta)+i\sin(\theta)\right)\] with \(r=5,\theta =\frac{3\pi}{2}\) if you choose that one

Answer 5

@satellite73

Answer 6

the answer is already provided in the posts, you might want to ask for clarification on something as opposed to just infering that we pick an answer for you ...

Answer 7

converting the radian 3pi/2 into degrees might help you pick the right option