Question

If (a + ib)2 = x + iy, find x2 + y2.​

Answer 1

Answer:

(a+ib)^2 = x + iy

a^2 + (ib)^2 + 2abi = x + iy

(a^2 - b^2) + 2abi = x+ iy

on comparing real and imaginary part,

x = a^2 - b^2

y = 2ab

now

we can proceed from here in two ways

first is simply evaluate x^2 + y^2 using the value of x and y.

second is as given below

x - iy = a^2 - b^2 - 2abi

= a^2 + (ib)^2 - 2abi

x - iy = (a - ib)^2

and it. was given that

x + iy = (a + ib)^2

multiplying the two eqns

(x+iy)(x-iy) = (a+ib)^2*(a-ib)^2

x^2 - (iy)^2 = {(a+ib)(a-ib)}^2

x^2 - i^2y^2 = (a^2 - i^2b^2)^2

x^2 + y^2 = (a^2 + b^2)^2 ( i^2 = -1)

Answer 2

Answer:

hope it helps you

Step-by-step explanation:

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