Question

Represent the complex number $Z=1+i$. in polar form.

Answer 1

$Z=1+i=\sqrt{2}(\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}})...........\left(1\right)$

Let Polar form of Given Equation be $Z=rcos\theta +irsin\theta ...............\left(2\right)$

Comparing (1) and (2)

we can write,

$rcos\theta =\sqrt{2}\ast \frac{1}{\sqrt{2}}=\sqrt{2}\cos {45}^{o}rsin\theta =\sqrt{2}\ast \frac{1}{\sqrt{2}}=\sqrt{2}\sin {45}^o$

$\therefore Z=\sqrt{2}(\cos {45}^o+i\sin {45}^o)$