Correct Answer - Option 1 : 0°
Concept:
The modulus of a complex number z = x + iy is given by:
|z| = \(\rm \sqrt{x^2+y^2}\)
The conjugate of z = z̅ = x - iy
The argument of the complex number z = x + iy is given by:
arg(z) = \(\rm \tan^{-1}({y\over x})\)
Calculation:
z = x + iy
\(\rm \overline z\)= x - iy
\(\rm z\cdot\overline z\) = (x + iy)(x - iy)
\(\rm z\cdot\overline z = x^2 -xyi+xyi-y^2i^2\)
\(\rm z\cdot\overline z = x^2 + y^2\)
arg(\(\rm z\cdot\overline z\)) = tan-1 \(\rm 0\over x^2+y^2\)
arg(\(\rm z\cdot\overline z\)) = 0
