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

1. The problem statement, all variables and given/known data

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

2. Relevant equations

sec (z) = 1/cos(z)

3. 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.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
 

HallsofIvy

Science Advisor
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1. The problem statement, all variables and given/known data

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

2. Relevant 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.

3. 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.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
 

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