Find the real and imaginary part of the complex number \(z=\frac{1-i}{i}\)

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:

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

Multiplying numerator and denominator by i

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

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

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

\(=-1-i\)

Re(z) = -1 

Im(z) = -1

Hence , option 4 is correct