Fsc Part 1 Mathematics (Complete Solution)

Q13
Prove that the sum as well as the product of any two conjugate complex numbers is a real number.

SOLUTION:

Let the two conjugate complex numbers are  a+bι , a-bι

Sum of two conjugate complex numbers = (a+bι) + (a-bι) which is real number
= a + ιb + a -ι b = 2a

Product of two conjugate complex numbers = (a+bι)(a-bι)

= (a)2-(bι)2

= a2-b2ι2

= a2-b2(-1)

= a2+b2

Both 2a and a2+b2 are real numbers.

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