- #1

r.a.c.

- 22

- 0

## Homework Statement

Q1: Express 962 as a sum of two squares (Hint: 962 = (13)(74)

Q2. Given z,a belong to C (complex). Find a such that the roots of the equation [tex] z^2 + az + 1 = 0 [/tex] have equal absolute values (or modulus).

## Homework Equations

Well this is about the complex plane so for the first one I think most probably its Euler's Identity. As for the second it could be anything.

## The Attempt at a Solution

Q1: It is a sum of squares so the best I can think of is that 962 is a modulus of a vector i.e. z belongs to C, |z| = 962. Because z = a + ib so [tex]962^2 = a^2 + b^2 [/tex]. Then I try writing z in polar so we have [tex]z = |z|e^i^x [/tex] , where x is the argument of z. But x = arctan b/a . So I somewhat got stuck in a loop.

Q2: We can't use the auxiliary equation because a is also complex. So it doesn't work. I tried expanding both z and a only to get stuck eventually in an overly complicated equation. Any suggestions on just how to start it?