Question

Find the real and imaginary part of the complex number \(\rm z=\frac {1-i}{1+i}\)
1. 1, 1
2. -1, 1
3. 0, 1
4. 0, -1

Answer 1

Correct Answer - Option 4 : 0, -1

Concept:

Equality of complex numbers.

Two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 are equal if and only if x1 = x2 and y1 = y2

Or Re (z1) = Re (z2) and Im (z1) = Im (z2).

 

Calculations:

Given complex number 

\(\Rightarrow z=\frac{1-i}{1+i}\)

Multiplying the numerator and denominator with 1 - i

\(\Rightarrow z=\frac{1-i}{1+i}\times \frac{1-i}{1-i}\)

\(\Rightarrow z=\frac{(1-i)(1-i)}{1-(i.i)}\)

\(=\frac{1+i^{2}-2i}{1+1}\)

\(=\frac{1-1-2i}{2}\)

= -i

So, z = 0 - i

∴ Re (z) = 0 and Im (z) = -1

Hence,option 4 is correct