(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let z1; z2; z3; z4 be four complex numbers on the unit circle (i.e., |z1|=|z2|=|z3|=|z4|=1).

It is known that z1+z2+z3+z4=1+i . Find the value of

1/z1

+

1/z2

+

1/z3

+

1/z4

2. Relevant equations

1/z = barZ/|z|^2

3. The attempt at a solution

I've been trying for about a day now and i just have no clue absolutely, I understand that

[b -a]/ [ab] = [1/a] - [1/b]

but i think there's something to do with conjugates or something this question is quite fustrating.

i also tried letting z1 + z2 + z3 + z4 = w

and then w*(barW) but i just got 0(1+i)(1-i) and then i cant take the inverse

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex numbers on unit circle

**Physics Forums | Science Articles, Homework Help, Discussion**