Concept Let z=x+ iy be a complex number, Where x is called the real part of the complex number or Re(z) and y is called the Imaginary part of the complex number or Im (z) Conjugate of z=z=x−iy Calculation: 1. The difference of Z and its conjugate is an imaginary number. Consider z=a+ib . . . (i) conjugate of z=z=a−ib... (ii) eq(i)−eq(ii) z−z=a+ib−a+ib =2ib Thus it is clear that the difference of z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate is a real number. eq (i)+eq(ii) z+z=a+ib+a−ib =2a Thus it is clear that the sum of Z and its conjugate is a real number. So, Both 1 and 2 are correct.