Correct Answer - Option 3 : x
2 + y
2
Concept:
The modulus of a complex number z = x + iy
|z| = \(\rm \sqrt{x^2+y^2}\)
The conjugate z̅ = x - iy
Calculation:
z = x + iy
z̅ = x - iy
z z̅ = (x + iy)(x - iy)
\(\rm z\cdot\overline z = x^2 -xyi+xyi-y^2i^2\)
\(\rm z\cdot\overline z = x^2 + y^2\)
\(\rm |z\cdot\overline z |= x^2 + y^2\)