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

  • #1

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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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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
[itex]e^{iz}+ e^{-iz}= -2i[/itex]
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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

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