vereinfachen e^{(ipi)/4}

Lösung

vereinfachen

e^{\frac{iπ}{4}}

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

Schritte zur Lösung

e^{\frac{iπ}{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

3 (2 x + 3) - 1 - 4 x = 4

∣ x ∣ = 0

- 6 y - 12 + 2 y = 28

f a c t or mn x^{2} + x y m^{2} + mn y^{2} + x y n^{2}

5 x^{2} = 8 x + 21