What is e^{(2pii)/8} ?

The solution to e^{(2pii)/8} is 1/(2^{1/2)}+i 1/(2^{1/2)}

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simplify e^{(2pii)/8}

simplify

e^{\frac{2 πi}{8}}

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

Solution steps

e^{\frac{2 πi}{8}}

\frac{2 πi}{8} = \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{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

t, a = p + p r t

96 \cdot 4

9 x^{2} - 18 x = 0

ln (3 x)

(46 t - 16 t^{2}) - 28

What is e^{(2pii)/8} ?
The solution to e^{(2pii)/8} is 1/(2^{1/2)}+i 1/(2^{1/2)}