If $${z_1}\,{\text{and }}{z_2}$$ are two non- zero complex numbers such that $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|,{\text{then arg }}{z_1} - {\text{arg }}{z_2}$$ is equal to
A.
$$\frac{\pi }{2}$$
B.
$$ - \pi $$
C.
$$0$$
D.
$$ \frac{ - \pi }{2}$$
Answer :
$$0$$
Solution :
$$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$
$$ \Rightarrow \,\,{z_1}\,{\text{and }}{z_2}$$ are collinear and are to the same side of origin; hence $${\text{arg }}{z_1} - {\text{arg }}{z_2} = 0.$$
Releted MCQ Question on Algebra >> Complex Number
Releted Question 1
If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$