Question

if θ is the amplitude of (a+ib)/(a-ib) ,then tanθ=

Answer 1

what do you mean by amplitude here?
a complex number has a magnitude and angle in polar coordinates?

Answer 2

for any complex number
\[x + yi\]
\[\tan \theta = \frac{y}{x}\]
\[\frac{a + bi}{a-bi} *\frac{a+bi}{a +bi} = \frac{(a^2 -b^2) + (2ab)i}{a^2 +b^2}\]
\[\tan \theta = \frac{\frac{2ab}{a^2 +b^2}}{\frac{a^2 -b^2}{a^2 +b^2}} = \frac{2ab}{a^2 - b^2}\]