Maths · Algebra · chapter 4 of 14

Class 11 Maths Chapter 4: Complex Numbers and Quadratic Equations Assertion-reason questions with answers

2 assertion-reason questions on Complex Numbers and Quadratic Equations, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): i is a solution of the equation x2 + 1 = 0. Reason (R): i2 = −1.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Putting x = i gives i² + 1 = −1 + 1 = 0, so A is true, and it is true exactly because i² = −1, which is R. So R explains A.

Question 2
Assertion (A): |3 + 4i| = |4 + 3i|. Reason (R): A complex number and its conjugate are mirror images of each other in the real axis.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Both moduli are √(9 + 16) = 5, so A is true. R is true, but 4 + 3i is not the conjugate of 3 + 4i (that is 3 − 4i); A holds because a² + b² does not change when a and b are interchanged. R does not explain A.

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