What is e^{-i pi/4} ?

The solution to e^{-i pi/4} is (sqrt(2))/2-i(sqrt(2))/2

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simplify e^{-i pi/4}

simplify

e^{- i \frac{π}{4}}

\frac{2}{2} - i \frac{2}{2}

Solution steps

e^{- i \frac{π}{4}}

Multiply

- i \frac{π}{4} : - \frac{πi}{4}

= e^{- \frac{πi}{4}}

Apply imaginary number rule:

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

= cos (- \frac{π}{4}) + i sin (- \frac{π}{4})

cos (- \frac{π}{4}) = \frac{2}{2}

sin (- \frac{π}{4}) = - \frac{2}{2}

Multiply

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

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

Apply rule

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

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

Rewrite

\frac{2 - 2 i}{2}

in standard complex form:

\frac{2}{2} - \frac{2}{2} i

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

- \frac{5}{2 ( 1 ^{\frac{3}{2}} )}

\frac{1}{x + 1} - \frac{1}{x + 3}

\frac{a}{a}

- 5 x + 10

(2 x - 3)^{2}