What is e^{-(ipi)/4} ?

The solution to e^{-(ipi)/4} is 1/(2^{1/2)}-i 1/(2^{1/2)}

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simplify e^{-(ipi)/4}

simplify

e^{- \frac{iπ}{4}}

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

Solution steps

e^{- \frac{iπ}{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{1}{2 ^{\frac{1}{2}}}

sin (- \frac{π}{4}) = - \frac{1}{2 ^{\frac{1}{2}}}

\frac{1}{2 ^{\frac{1}{2}}} i = \frac{i}{2 ^{\frac{1}{2}}}

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

Apply rule

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

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

Rewrite

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

in standard complex form:

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

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

9 x^{3} y - 64 x y^{3}

2 x - 4 x = - 5

4 - \frac{1}{3}

2 t^{2} - 12 t - 14

4 a < 40

What is e^{-(ipi)/4} ?
The solution to e^{-(ipi)/4} is 1/(2^{1/2)}-i 1/(2^{1/2)}