Find Real Values of k for Purely Real ##u##

[squenshl]

Homework Statement

Find all possible values of $k$ that make $u = \frac{k+4i}{1+ki}$ a purely real number.

Homework Equations

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.

 

[PeroK]

Homework Statement

Find all possible values of $k$ that make $u = \frac{k+4i}{1+ki}$ a purely real number.

Homework Equations

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.

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?

 

[squenshl]

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

 

[PeroK]

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

It does look good!