# NCERT Class 11 Mathematics Solutions: Chapter 5 – Complex Number and Quadratic Equations Miscellaneous Exercise Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. Find the real numbers x and y if is the conjugate of

Answer:

Consider,

It is given that,

Equating real and imaginary parts, we obtain

… eq (i)

… eq (ii)

Multiplying equation (i) by and equation (ii) by and then adding them, we obtain

Putting the value of x in equation (i)

So, the values of and are and respectively.

2. Find the modulus of

Answer: