Question

The principal value of the amplitude of (1 + i) is
(a) $\frac{\mathrm{\pi }}{4}$
(b) $\frac{\mathrm{\pi }}{12}$
(c) $\frac{3\mathrm{\pi }}{4}$
(d) π

Answer 1

(a)$\frac{\pi }{4}$

Let z = (1+i)
$$\begin{gathered} \tan \alpha =\left|\frac{\mathrm{Im}\left(z\right)}{\mathrm{Re}\left(z\right)}\right| \\ =1 \\ \Rightarrow \alpha =\frac{\mathrm{\pi }}{4} \\ \mathrm{Since},z\mathrm{lies}\mathrm{in}\mathrm{the}\mathrm{first}\mathrm{quadrant}. \end{gathered}$$
Therefore, arg (z) = $\frac{\pi }{4}$