Question

Question 11 If a + ib = (x+i)^2 / (2x^2 +1), prove that a^2 + b^2 = (x^2 + 1)^2 / (2x+1)^2

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 113

Answer 1

(a + ib) = (x + i)²/(2x²+1) ,
take modulus both sides,
|a + ib| = |(x + i)²|/|(2x²+1)|

we know,
|zⁿ| = |z|ⁿ also |+ve number| = +ve number

√(a² + b²) = |x + i|²/(2x²+1)
√(a² + b²) = (√(x² + 1))²/(2x²+1)
squaring both sides,
(a² + b²) = (x² +1)/(2x²+1)²
Hence, proved

Answer 2

Step-by-step explanation:

this is the answer ...............