Hello! I was doing some alcumus, and I came upon a review problem: (A problem that you can't skip), and it was about conjugates in intermediate algebra. I have fun doing alcumus, and I recommend playing it, but I came across this problem. This does not require much work, but I never quite learned about conjugates so I need your help :D

If |z| = 1, express $\overline{z}$ as a simplified fraction in terms of z.

Thanks in advance!

OofPirate Apr 23, 2021

#1**+1 **

Hello :))

I'm not quite sure how to do it either, but I'll try my best to help.

A conjugate is like an inverse, a+ bi conjugate is a - bi.

The absolute value of a complex number is sqrt(a^2 + b^2), a + bi.

So we have a complex number (a+bi) where sqrt(a^2 + b^2) = 1.

z = a + bi

sqrt(a^2 + b^2) = 1

a^2 + b^2 = 1

We're looking for a - bi in terms of z.

(a-bi)(a+bi) = a^2 + b^2

But we know a^2 + b^2 = 1.

(a-bi)(a+bi) = 1

We also know that a + bi = z.

(a-bi)(z) = 1

a-bi = 1/z

Our answer is 1/z hopefully

I hope this helped. :))

=^._.^=

catmg Apr 23, 2021