+115 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!
+2407 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. :))
=^._.^=
