UPSC NDA I 2021 Mathematics Solved Paper

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.