(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

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# Complex numbers on unit circle

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