Find z when sec(z) = 3i

[Questioneer]

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]

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)= (e^iz+ e^-iz)/2. So you have
[tex]\frac{2}{e^z+ e^{-z}}= i[/itex]<br /> which can be reduced to <br /> $e^{iz}+ e^{-iz}= -2i$<br /> and that can be converted to a quadratic.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <h2>The Attempt at a Solution</h2><br /> <br /> 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? </div> </div> </blockquote> Don't assume things!<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Thanks in advance. </div> </div> </blockquote>[/tex]