Given-tbat-Arg-z-1-6-and-Arg-z-1-2-3-Find-z-please-help-me-

Question Number 152091 by rexford last updated on 25/Aug/21

G i v e n t b a t A r g (z + 1) = \frac{Π}{6} a n d

A r g (z - 1) = \frac{2 Π}{3} . F i n d z .

p l e a s e h e l p m e

Answered by Olaf_Thorendsen last updated on 25/Aug/21

Let z = x + i y

Arg (z + 1) = \frac{π}{6} \Rightarrow \frac{y}{x + 1} = \tan \frac{π}{6} = \frac{1}{\sqrt{3}} (1)

Arg (z - 1) = \frac{2 π}{3} \Rightarrow \frac{y}{x - 1} = \tan \frac{2 π}{3} = - \sqrt{3} (2)

(1) : y = \frac{x + 1}{\sqrt{3}}

(2) : \frac{x + 1}{\sqrt{3}} = - \sqrt{3} (x - 1)

x = \frac{1}{2} \Rightarrow y = \frac{\frac{1}{2} + 1}{\sqrt{3}} = \frac{\sqrt{3}}{2}

z = x + i y = \frac{1}{2} + \frac{\sqrt{3}}{2} i = e^{i \frac{π}{3}}

Commented by rexford last updated on 27/Aug/21

t h a n k y o u

Facebook Tweet Pin