Q. 24

Mark the Correct alternative in the following:

If x + i y = (1 + i) (1 + 2 i) (1 + 3i), then x2 + y2 =

A. 0

B. 1

C. 100

D. None of these

Answer :

Given that (1 + i) (1 + 2i) (1 + 3i) = x + i y …(1)

We can also say that


(1 - i) (1 - 2i) (1 - 3i) = x - i y …(2)


Multiply and divide the eq no. 2 with eq no. 1



((1)2 – (i)2)((1)2 – (2i)2)((1)2 – (3i)2) = ((x)2 – (iy)2)


x2 + y2 = 2 × 5 × 10 = 100

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