thomas49th
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Homework Statement
The complex number z is defined by
z = \frac{a+2i}{a-i}
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
\frac{a^{2} + 3ai + 1}{a^{2}-1}
Now the real part is going to be a² + 1
so i set
\frac{a^{2} + 1}{a^{2} - 1} = \frac{1}{2}
however I get a = \sqrt{-3}
Have I gone the right way about solving this question?
Thanks :)