Let  z₁ = 2 - i, z₂ = -2 + i . Find
(i) Re (z₁z₂/z₁') (ii) Im (1/z₁z₁')

Solution:

(i) Re (z₁z₂/z₁') = Re ( (2 - i) (-2 + i) / (2 + i))

= Re ((-4 + 1 + 4i) / (2 + i))

= Re ( (-3 + 4i) / (2 + i) )

= Re ( (-3 + 4i) / (2 + i) · (2 - i) / (2 - i) ) (Rationalized the denominator)

= Re ( (-6 +11i + 4) / (4 + 1))

= Re ((-2+11i) / 5)

= -2/5

(ii) Im (1/z₁z₁') = Im ( 1 /((2-i)(2+i)) )

= Im ( 1 / (4 + 1) )

= Im (1/5) 

= 0

Thus, i) The value of Re (z₁z₂/z₁') is equal to -2/5, (ii) The value of Im (1/z₁z₁') is 0

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NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 12

Let  z₁ = 2 - i, z₂ = -2 + i . Find (i) Re (z₁z₂/z₁') (ii) Im (1/z₁z₁')

Summary:

i) The value of Re (z₁z₂/z₁') is equal to -2/5, (ii) The value of Im (1/z₁z₁') is 0