Question

please answer the question

Answer 1

Hi there!
Here's the answer:


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Given,
(a + ib)(c + id) = x + iy

First solving LHS part

=> ac + iad + ibc + i²bd
=> ac + iad + ibc - bd

°•° i² = -1

Separate real & Imaginary terms

=> (ac - bd) + i(ad + bc)


As per the data,
(ac - bd) + i(ad + bc) = x + iy

On comparing Both sides

We get
x = ac - bd
y = ad + bc



Now,
L.H.S = (a² + b²)(c² + d²)
= (a²c² + a²d² + b²c² + b²d²)



R.H.S = x² + y²
Substitute x & y

= (ac - bd)² + (ad + bc)²

= a²c² + b²d² - 2abcd + a²d² + b²c² + 2abcd

= a²c² + b²d² + a²d² + b²c²



•°• LHS = RHS



Hence proved

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Hope it helps