Solveeit Logo
Login

Question

Question: If \(\arg\left( \frac{3 + i}{2 - i} + \frac{3 - i}{2 + i} \right)\), then \(\frac{\pi}{2}\)...

If arg⁡(3+i2−i+3−i2+i)\arg\left( \frac{3 + i}{2 - i} + \frac{3 - i}{2 + i} \right), then π2\frac{\pi}{2}

A

−π2- \frac{\pi}{2}

B

π4\frac{\pi}{4}

C

z1.z2........zn=z,z_{1}.z_{2}........z_{n} = z,

D

arg⁡z1+argz2+....\arg z_{1} + argz_{2} + ....

Answer

z1.z2........zn=z,z_{1}.z_{2}........z_{n} = z,

Explanation

Solution

arg⁡(z1zˉ2)=arg⁡z1−arg⁡(zˉ2)=arg⁡z1+arg⁡z2\arg \left( \frac { z _ { 1 } } { \bar { z } _ { 2 } } \right) = \arg z _ { 1 } - \arg \left( \bar { z } _ { 2 } \right) = \arg z _ { 1 } + \arg z _ { 2 } tan⁡−101=0\tan^{- 1}\frac{0}{1} = 0

Option (3) gives the same result.