Consider the following

1. zz̅ = |z|2

2. z-1 = , where z = complex number 

Which of the above statement is/are correct?

  1. Only 1
  2. Only 2
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer (Detailed Solution Below)

Option 1 : Only 1
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

Concept:

Consider a complex number, z = a + ib

Conjugate of complex number = z̅ = a - ib

Modulus of complex number  = |z| = 

Calculation: 

Let, z = a + ib,

zz̅ = (a + ib)(a - ib)

=

=

And, |z|2 = 

∴ zz̅  = |z|2

Now, 

 

=

 ≠ 

Hence, option (1) is correct.

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