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!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Purely Real Proof Date
"Arithmetic?" proof Jan 28, 2015
A level Further Pure Maths help (Polynomials) Sep 19, 2010
Pure mathematics problem Oct 10, 2009
Math 30 Pure June 2008 Diploma Jul 8, 2008