Consider the following statements in respect of an arbitrary complex number Z : 1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate is a real number. Which of the above statements is/are correct?

NDA 2021 Mathematics question

Consider the following statements in respect of an arbitrary complex number : 1. The difference of and its conjugate is an imaginary number. 2. The sum of and its conjugate is a real number. Which of the above statements is/are correct?

(A)1 only
(B)2 only
(C)Both 1 and 2Correct
(D)Neither 1 nor 2

Answer: (C)

Solution

Let , so . Statement 1: , which has zero real part, i.e. it is a purely imaginary number (it reduces to only

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Question ID VK-033531