The problem involves finding values of ##k## that make the expression ##u = \frac{k+4i}{1+ki}## a purely real number. This falls under the subject area of complex numbers and their properties.
The discussion is active, with participants confirming their calculations and exploring the implications of their findings. There is an exchange of ideas regarding the method of using the conjugate and checking specific values.
Participants are working under the assumption that the expression must yield a purely real number, and there is a focus on the implications of the complex conjugate in this context.
Did you try setting ##k= \pm 2## in the original number to see whether you get a real number?squenshl said: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.
It does look good!squenshl said:Yes to the first and yes to the second (conjugate of the denominator though) and it looks all good!