Question

Find the argument
$(1 + i)( \sqrt{3} + i)$
​

Answer 1

Step-by-step explanation:

arg((1+i)(√3+i)) => arg(1+i)+arg(√3+i)

(1+i) =√2(1/√2 +i/√2) =

√2(cos(45°)+i(sin(45°)) =

$\sqrt{2} {e}^{i \frac{\pi}{4} }$

√3+i =>2(√3/2 +i/2) =2(cos(60°)+i(sin(60°))

$= 2 {e}^{i \frac{\pi}{3}}$

Hence arg(1+i)(√3+i) = π/3 +π/4 = 3π+4π/12

= 7π/12 = 105°. Hope it helps you.