Question

√(e^(iπ/3)) Perform calculations and give answer in Cartesian form.

Answer 1

\[\sqrt{e^{i\pi/3}}=\left(e^{i\pi/3}\right)^{1/2}=e^{i\frac{3\pi}{2}}=\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2}=\cdots\]

Answer 2

and thts it?

Answer 3

-i?

Answer 4

thts not the right answer though...

Answer 5

the answer is √3 / 2 +i/2 but idk how you got tht...

Answer 6

Oh, sorry, my bad. I misread the question the second time around...
\[\sqrt{e^{i\pi/3}}=\left(e^{i\pi/3}\right)^{1/2}=e^{i\color{red}{\frac{\pi}{6}}}=\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}=\cdots\]

Answer 7

its e to the power i pi/3

Answer 8

kk well thnks anyways. just needed to check my work

Answer 9

Right, I just made a mistake with the fraction in the numerator. \(\dfrac{\pi}{3}\cdot\dfrac{1}{2}=\dfrac{\pi}{6}\).