# Homework Help: Purely Real Proof

1. Dec 1, 2017

### squenshl

1. The problem statement, all variables and given/known data
Find all possible values of $k$ that make $u = \frac{k+4i}{1+ki}$ a purely real number.

2. Relevant equations

3. The attempt at a solution
I calculated the complex conjugate which was $\frac{5k}{k^2+1} + \frac{4-k^2}{k^2+1}i$. So to prove this do I just solve $\frac{4-k^2}{k^2+1}$ = 0 for $k$???
In this case $k = \pm 2$. Thanks.

2. Dec 1, 2017

### PeroK

Did you try setting $k= \pm 2$ in the original number to see whether you get a real number?

Did you mean you multiplied the denominator and numerator by the conjugate of the numerator?

3. Dec 1, 2017

### squenshl

Yes to the first and yes to the second (conjugate of the denominator though) and it looks all good!!!

4. Dec 1, 2017

### PeroK

It does look good!