Fsc Part 1 Mathematics (Complete Solution)

Q4
Prove that

Z = z    iff z is real

SOLUTION: Z = z  ------->(EQ 1)

Let    Z = a-bι            and    z=a+bι

By putting the value of z and Z in eq 1,we get.

a-bι  = a+bι

  a-bι  -a-bι  =0

a-a-bι-bι=0

0-2bι=0

-2bι=o

b=0

∴ z=a+0=a. this is shows that z is real.

Conversly, suppose z is real no. 

then z=a+0=a  , a ∈ℝ and  Z=a-0=a,   a ∈ℝ

therefore a=a  

hence Z=z

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