The magnitude and amplitude of ((1+i√3)(2+2i)/(√3-i)) are respectively

Question

The magnitude and amplitude of ((1+i√3)(2+2i)/(√3-i)) are respectively (A)  2,(3π /4)  (B)  4,(3π /4)  (C)  2√2,(π /4)  (D)  2√2,(π /2)

Tardigrade Admin · Accepted Answer

((1+i√3)(2+2i)/(√3-i))=(2+2i+2√3i-2√3/(√3-i)) =( (2-2√3)+2i(1+√3) /(√3-i))× ((√3+i)/(√3+i)) =(2√3-6+2i-2√3i+2√3i+6i-2-2√3/3+1) =(-8+8i/4)=-2+2i ∴ Magnitude of ((1+i√3)(2+2i)/(√3-i)) =√4+4=2√2 and amplitude of ((1+i√3)(2+2i)/(√3-i)) = tan -1( (2/-2) )=(3π /4)

Q. The magnitude and amplitude of $\frac{( 1 + i 3 ) ( 2 + 2 i )}{( 3 - i )}$ are respectively

$2, \frac{3 π}{4}$

$4, \frac{3 π}{4}$

$22, \frac{π}{4}$

$22, \frac{π}{2}$

$22, \frac{3 π}{4}$

Q. The magnitude and amplitude of (3​−i)(1+i3​)(2+2i)​ are respectively

2,43π​

4,43π​

22​,4π​

22​,2π​