NCERT Class 11 Mathematics Solutions: Chapter 5 – Complex Number and Quadratic Equations Miscellaneous Exercise Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Definition of Complex Numbers

1. Find the number of non-zero integral solutions of the equation


So, is the only integral solution of the given equation.

So, the number of nonzero integral solutions of the given equation is .

2. If , then show that: .


On squaring both sides, we obtain


So, proved.

3. If then find the least positive integral value of .


where is some integer.

So, the least positive integer is .

The least positive integral value of m is .

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