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

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

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simplify e^{(2ipi)/3}

simplify

e^{\frac{2 iπ}{3}}

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

Solution steps

e^{\frac{2 iπ}{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

∣ x + 4 ∣ = 3 x

8 x^{2} y^{2} + 20 x y^{2} - 28 x^{3} y^{4}

x^{4} - a^{4}

13!

2 b^{2} + 29 b + 90