Question

Find the argument of the zz' where z = 2i +4 and z' is the conjugate of z.
1. 0°
2. tan-1(2)
3. tan-1(\(1\over 2\))
4. 90°

Answer 1

Correct Answer - Option 1 : 0°

Concept: 

The argument of a complex number z = x + iy

arg(z) = tan-1\(\rm \left(y\over x\right)\)

 

Calculation:

z = 2i + 4 = 4 + 2i

Conjugate of z = z' = 4 - 2i = -2i + 4

zz' = (2i + 4) ×(-2i + 4)

zz' = -4i² - 8i + 8i + 16

zz' = 4 + 16 = 20 + 0i 

∴ x = 20, y = 0

arg(zz') = tan^-1(\(0\over 20\))

arg(zz') = tan^-1 (0) = 0°