Question

if x+¡y=1-¡/1+¡,then x^2+y^2 is equal to​

Answer 1

Used Formulas :

1. (a - b)² = a² - 2ab + b²

2. (a + b) (a - b) = a² - b²

3. i² = - 1 , where i is the squared root of (- 1)

Solution :

Now, (1 - i) / (1 + i)

by multiplying both the numerator and the denominator by (1 - i) we get

= {(1 - i) (1 - i)} / {(1 + i) (1 - i)}

= (1² - 2i + i²) / (1² - i²)

= (1 - 2i - 1) / {1 - (- 1)}

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

= (- 2i) / 2

= - i

Given that, x + iy = (1 - i) / (1 + i)

⇒ x + iy = - i

⇒ x + iy = 0 + i (- 1)

Comparing among the coefficients from both sides, we get

x = 0 , y = - 1

Therefore, x² + y²

= 0² + (- 1)²

= 0 + 1

= 1