- #1
thomas49th
- 655
- 0
Homework Statement
The complex number z is defined by
[tex]z = \frac{a+2i}{a-i}[/tex]
Given that the real part of z is 1/2, find the value of a
Homework Equations
The Attempt at a Solution
Well first of all i multiplied the numerator and denominator of z by (a+i)
which gave me
[tex]\frac{a^{2} + 3ai + 1}{a^{2}-1}[/tex]
Now the real part is going to be a² + 1
so i set
[tex]\frac{a^{2} + 1}{a^{2} - 1} = \frac{1}{2}[/tex]
however I get a = [tex]\sqrt{-3}[/tex]
Have I gone the right way about solving this question?
Thanks :)