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

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

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simplify e^{-(ipi)/3}

simplify

e^{- \frac{iπ}{3}}

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

Solution steps

e^{- \frac{iπ}{3}}

Apply imaginary number rule:

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

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

cos (- \frac{π}{3}) = \frac{1}{2}

sin (- \frac{π}{3}) = - \frac{3}{2}

Multiply

\frac{3}{2} i : \frac{3 i}{2}

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

Rewrite

\frac{1 - 3 i}{2}

in standard complex form:

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

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

k^{4} + 10 k^{3} + 35 k^{2} + 50 k + 24

x + 2 = 2 x - 1

9 (b + 7) = 72

(\frac{8}{9})^{3}

\frac{4 a ^{2} - 36 a}{2 a ^{4} - 24 a ^{3} + 54 a ^{2}}