Need help with a quadratic that has complex roots

This is the equation in question:

I'm out of practice for these and don't remember how best to handle this. If I plug it into the quadratic equation, I get a square root that I'm not sure how to simplify. I'm guessing I need to apply Euler's Formula, but again, I'm out of practice.

I know the answer to this is:

...I'm just not sure how to get there.

Can someone give me a hand?

Re: Need help with a quadratic that has complex roots

Hey Lancet.

Try multiplying both sides by z^2 and consider anything not a z as a constant (if it is a constant). You then get something along the lines of az^2 + bz + c = 0.

Re: Need help with a quadratic that has complex roots

I would first multiply through by and write in standard form:

Apply the quadratic formula:

Now, apply Euler's formula to obtain:

Re: Need help with a quadratic that has complex roots

Quote:

Originally Posted by

**MarkFL2**
Apply the quadratic formula:

Ah! That's where I was getting stuck. I didn't know what to do with

I didn't realize that was a modified trig identity. Thanks!