Complex Numbers...

Find the conjugate of \(\frac{1+ i }{1- i }\).

The argument of the complex number \(\frac{1+ i }{1- i }\), where \(i =\sqrt{-1}\), is:

Find \(\frac{z_{1}}{z_{2}}\), when \(z_{1}=6+2 i\) and \(z _{2}=2- i\).

If tan α and tan β are the roots of the equation x² - 4x - 3 = 0, then the value of (α + β) is:

If \({x}+{iy}=\frac{3+4 {i}}{2-{i}}\) where \({i}=\sqrt{-1}\), then what is the value of y?

What is the modulus of \(\frac{1+7 i }{(2- i )^{2}}\)?

Find conjugate of \(\frac{3+2 i }{2- i }\).

What is the value of \((-1+i \sqrt{3})^{48}\)?

If \(\alpha, \beta\) are the roots of the equation \(x^{2}+x+2=0\), then \(\frac{\alpha^{10}+\beta^{10}}{\alpha^{-10}+\beta^{-10}}\) is equal to: