write-1-i-23-3-i-13-by-re-i-such-that-r-gt-0-pi-lt-pi-

Question Number 132655 by mohammad17 last updated on 15/Feb/21

w r i t e \frac{{(1 - i)}^{23}}{{(\sqrt{3} - i)}^{13}} b y {r e}^{i θ} s u c h t h a t r > 0, - π ⩽ θ < π

Answered by physicstutes last updated on 15/Feb/21

1 - i = \sqrt{2} e^{- \frac{π}{4} i}

\Rightarrow {(1 - i)}^{23} = \sqrt{2}^{23} e^{- \frac{23 π}{4} i}

\sqrt{3} - i = 2 e^{- \frac{π}{6} i} \Rightarrow {(\sqrt{3} - i)}^{13} = 2^{13} e^{- \frac{13 π}{6} i}

z = \frac{2048 \sqrt{2} e^{- \frac{23 π}{4} i}}{2048 \times 4 e^{- \frac{13 π}{6} i}} = \frac{\sqrt{2}}{4} e^{- \frac{43 π}{12} i}

Commented by MJS_new last updated on 15/Feb/21

wrong format . \frac{\sqrt{2}}{4} e^{\frac{5 π}{12} i} is the right answer

Commented by mohammad17 last updated on 16/Feb/21

c a n y o u s o l v e t h i s s i r

Commented by physicstutes last updated on 16/Feb/21

yes yes sir, thank you, i just saw that