NCERT Class 11 Mathematics Solutions: Chapter 5 – Complex Number and Quadratic Equations Miscellaneous Exercise Part 7 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. Let . Find

(i)

(ii)

On multiplying numerator and denominator by , we obtain

On comparing imaginary parts, we obtain

2. Find the modulus and argument of the complex number

Consider,

Consider

i.e.. ,

On squaring and adding, we obtain

[Conventionally, ]

[As lies in the II quadrant]

So, the modulus and argument of the given complex number are respectively.