Question

how do you find the argument of z when expressing a complex number in trigonometriic functions

Answer 1

i know that z=-2

Answer 2

and i know z=r(cos theta+i sin theta)

Answer 3

so it would be \[2(\cos \theta +i \sin \theta)\]

Answer 4

but i need to know how to find theta
which i know it says \[\tan^{-1} b/a\]

Answer 5

but i dont know how to get b or a

Answer 6

For purely imaginary or real numbers, you can easily pinpoint the argument using a diagram like the one below: