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

#### Questioneer

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?

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

2. Relevant equations

3. The attempt at a solution

Related Calculus and Beyond Homework News on Phys.org

#### HallsofIvy

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
$e^{iz}+ e^{-iz}= -2i$
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!

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

2. Relevant equations

3. The attempt at a solution

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

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving