What is e^{(2pii)/3} ?

The solution to e^{(2pii)/3} is -1/2+i(sqrt(3))/2

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simplify e^{(2pii)/3}

simplify

e^{\frac{2 πi}{3}}

- \frac{1}{2} + i \frac{3}{2}

Solution steps

e^{\frac{2 πi}{3}}

Apply imaginary number rule:

e^{ia} = cos (a) + i sin (a)

= cos (\frac{2 π}{3}) + i sin (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= - \frac{1}{2} + \frac{3}{2} i

5162 - 38

\frac{2 a}{3 - a} + \frac{1}{5 ( a + 2 )}

12 x - 18

lo g_{14} (1)

lo g_{\frac{1}{9}} (3)