# [Homework Help!] Find the value of z when sec(z) = 3i.

## Homework Statement

Find the value of z when sec(z) = 3i.

## Homework Equations

sec (z) = 1/cos(z)

## The Attempt at a Solution

I assume that I need to transform into polar coordinates and then use some transformations. I'm really at a loss. If not a solution maybe a few hints to go in the right direction?

Thanks in advance.

HallsofIvy
Science Advisor
Homework Helper

## Homework Statement

Find the value of z when sec(z) = 3i.

## Homework Equations

sec (z) = 1/cos(z)
Good start. And, since you are working with complex numbers, cos(z)= (eiz+ e-iz)/2. So you have
[tex]\frac{2}{e^z+ e^{-z}}= i[/itex]
which can be reduced to
$e^{iz}+ e^{-iz}= -2i$
and that can be converted to a quadratic.

## The Attempt at a Solution

I assume that I need to transform into polar coordinates and then use some transformations. I'm really at a loss. If not a solution maybe a few hints to go in the right direction?
Don't assume things!

Thanks in advance.