Help with re^1theta form

[barren falcon]

Could anyone guide me to solve this problem please

[latent jacinth]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

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3. Feel free to nominate the person for helper of the week in #helper-nominations

[drifting oar]

Firstly, this isn't calculus, this is algebra. In the future, please don't mistag your posts. \ \ For convenience, I'll call $z=-\frac{11\sqrt 3}{2}+\frac{11}{2}i$. \ \ We know that $|z|=\sqrt{\left(-\frac{11\sqrt 3}{2} \right)^2+\left(\frac{11}{2} \right)^2}=11$. \ \ Furthermore, the argument of $z$ is $\frac{5\pi}{6}$, which can be verified by sketching a diagram and observing the argument is $\pi-\arcsin \left(\frac{1}{2} \right)$. \ \ \ So, we need to find $(11e^{5i\pi/6})^{1/4}$, which is $11^{1/4}e^{\frac{5i\pi}{24}}$.

[arctic granite]

civil_service_pigeon

[barren falcon]

Hey, I realized it was algebra but this problem is part of my "pre-calc" course so I sorted it in both algebra and calc. As for the problem, thank you :) This does help me a bit