Originally Posted by

**sqleung** Can somebody please help me with this problem?

==================================

**Find the complex number $\displaystyle z$ that satisfies the equation:**

$\displaystyle \frac {25}{z} - \frac {15}{\bar z} = 1 - 8i$

Given $\displaystyle \bar z$ is the conjugate of $\displaystyle z$ and $\displaystyle |z| = 2\sqrt{5}$

==================================

This is what I've done so far:

Let $\displaystyle z = a + bi$

Therefore: $\displaystyle \bar z = a - bi$

$\displaystyle \sqrt {a^2 + b^2} = 2\sqrt{5}$

$\displaystyle a^2 + b^2 = 20$

$\displaystyle a^2 = 20 - b^2$

$\displaystyle a = \sqrt {20 - b^2}$

---

$\displaystyle \frac {25}{a + bi} - \frac {15}{a - bi} = 1 - 8i$

$\displaystyle \frac {25}{\sqrt {20 - b^2} + bi} - \frac {15}{\sqrt {20 - b^2} - bi} = 1 - 8i$

-------------------------------------------------

Should I continue or should I stop before I start stuffing everything up? Is this correct? If not, could you please show me how to continue on?

Thank you - all help is of course, appreciated.