complex numbers

Consider the following expression: $z = \sin(y+it)+\cos(y-it)$ where z, y, and t are variables, and $i=\sqrt{-1}$ is a complex number. The partial differential equation derived fro...

Given $$i = \sqrt { - 1} ,$$ the value of the definite integral, $$\,{\rm I} = \int\limits_0^{\pi /2} {{{\cos x + \sin x} \over {\cos x - i\,\sin x}}dx\,\,} $$ is :

$$z = {{2 - 3i} \over { - 5 + i}}$$ can be expressed as

The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is

Which one of the following is not true for the complex number z 1 and z 2 ?