if-z-1-z-2-z-3-1-and-1-z-1-1-z-2-1-z-3-1-find-z-1-z-2-z-3-z-1-z-2-z-3-complex-number-

Question Number 130818 by Study last updated on 29/Jan/21

i f ∣ z_{1} ∣=∣ z_{2} ∣=∣ z_{3} ∣= 1

a n d ∣ \frac{1}{z_{1}} ∣ + ∣ \frac{1}{z_{2}} ∣ + ∣ \frac{1}{z_{3}} ∣= 1

f i n d ∣ z_{1} + z_{2} + z_{3} ∣= ?

z_{1}, z_{2}, z_{3} \in c o m p l e x n u m b e r

Answered by TheSupreme last updated on 29/Jan/21

z_{i} = ρ_{i} e^{i θ_{i}}

ρ_{1} = ρ_{2} = ρ_{3} = 1

\frac{1}{ρ_{1}} + \frac{1}{ρ_{2}} + \frac{1}{ρ_{3}} = 1

3 = 1

i m p o s s i b l e

w e c a n e v a l u a t e

\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} = 1

e^{- i θ_{1}} + e^{- i θ_{2}} + e^{- i θ_{3}} = 1

t h e n

e^{i θ_{1}} + e^{i θ_{2}} + e^{i θ_{3}} = {(e^{i θ_{1}} + e^{i θ_{2}} + e^{i θ_{3}})}^{*} = 1^{*} = 1

Commented by Study last updated on 30/Jan/21

t h a n k s s i r

Facebook Tweet Pin