Question

If z = 2i +1, find the value of \(\rm\left| z + \overline z +1\over z + \overline z -1\right|\), where \(\rm \overline z\) is the conjugate of the complex number z
1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 3 : 3

Concept:

The modulus of a complex number z = x + iy

|z| = \(\rm \sqrt{x^2+y^2}\)

The conjugate \(\rm \overline z\) = x - iy

Calculation:

z = 1+ 2i

\(\rm \overline z\)= 1 - 2i

S = \(\rm\left| z + \overline z +1\over z + \overline z -1\right|\)

S = \(\rm\left| 1+2i+1-2i+1\over 1+2i+1-2i -1\right|\)

S = \(\rm\left| 3\over 1\right|\) 

S = 3