vereinfachen e^{(2pii)/8}

Lösung

vereinfachen

e^{\frac{2 πi}{8}}

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

Schritte zur Lösung

e^{\frac{2 πi}{8}}

\frac{2 πi}{8} = \frac{πi}{4}

= e^{\frac{πi}{4}}

Wende imaginäre Zahlenregel an:

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}}}

Wende Regel an

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

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

Schreibe

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

in der Standard komplexen Form um:

\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

so l v e f or t, a = p + p r t

9 x^{2} - 18 x = 0

s im pl i f y ln (3 x)

f a c t or (46 t - 16 t^{2}) - 28

s im pl i f y 1.5 \times 1 0^{- 5}