Question

If a + ib = c + id then
1. a² + c² = 0
2. b² + c² = 0
3. b² + d² = 0
4. a² + b² = c² + d² 
5.

Answer 1

Correct Answer - Option 4 : a² + b² = c² + d² 

Concept:

If z = x + iy

Where,

x and y are real and imaginary parts of z and

i = √-1 

Modulus of z:

|z| = \(\sqrt{x^2\ +\ y^2}\)

Calculation:

Given that

a + ib = c + id

Taking modulus of both side

⇒ |a + ib| = |c + id|

⇒ \(\sqrt{a^2\ +\ b^2}\ =\ \sqrt{c^2\ +\ d^2}\)

⇒ a2 + b2 = c2 + d2