Archit's Challenge 1

Algebra Level 4

11 z 10 + 10 i z 9 + 10 i z − 11 = 0 11z^{10} + 10iz^9 + 10iz - 11 = 0

Find the number of possible values of ∣ z ∣ |z| , where z z is a complex number .

Notation: i = − 1 i=\sqrt{-1} is the imaginary unit .

2 4 0 1 3

Archit Agrawal by Archit Agrawal , 21, India

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2 solutions

Archit Agrawal
Nov 28, 2015

3 Helpful 0 Interesting 0 Brilliant 0 Confused

You have shown that if a solution exists, ∣ z ∣ = 1 \left| z \right| =1 . For completeness, you should show that there is infact a solution to the equation above.

Aditya Dhawan - 4 years, 7 months ago
Vilakshan Gupta
Mar 10, 2021

See solutions here , here or here .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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