Least positive argument of the 4 text th root of the complex number 2-i √12 is

Question

Least positive argument of the 4 text th root of the complex number 2-i √12 is (A) π / 6 (B) 5 π / 12 (C) 7 π / 12 (D) 11 π / 12

Tardigrade Admin · Accepted Answer

z4=2(1-√3 i)=4((1/2)-(√3/2) i) =4[ cos (-(π/3))+i sin (-(π/3))] z=√2[ cos (2 m π-(π / 3)/4)+i sin (2 m π-(π / 3)/4)] For m=1, z=√2[ cos ((5 π/12))+i sin ((5 π/12))].

Q. Least positive argument of the $4^{th}$ root of the complex number $2 - i 12$ is

$π /6$

$5 π /12$

$7 π /12$

$11 π /12$

$z^{4} = 2 (1 - 3 i) = 4 (\frac{1}{2} - \frac{3}{2} i)$
$= 4 [cos (- \frac{π}{3}) + i sin (- \frac{π}{3})]$
$z = 2 [cos \frac{2 mπ - ( π /3 )}{4} + i sin \frac{2 mπ - ( π /3 )}{4}]$
For $m = 1, z = 2 [cos (\frac{5 π}{12}) + i sin (\frac{5 π}{12})]$ .

Q. Least positive argument of the 4th root of the complex number 2−i12​ is

π/6

5π/12

7π/12

11π/12