Question

If x=a+ib and y=a-ib then xy =?

Answer 1

Answer:

a²+b²

Step-by-step explanation:

(a+ib)(a-ib)

a² +iab-iab-i²b²

a²-i²b²

a²-(-1)b

a²+b²

Answer 2

The value of xy is (a²+b²)

Given : The given values are, x = a+ib and y = a-ib

To find : The value of xy

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of xy)

Here,

The value of i is √(-1)

(with this value of i we have to calculate the value of the given expression)

So,

= xy

= x × y

= (a+ib) × (a-ib)

= (a)² - (ib)² [As, (x+y) × (x-y) = x²-y²]

= a² - (i²b²)

= a² - [(√-1)² × b²]

= a² - [(-1) × b²]

= a² - (-b²)

= a²+b²

(This will be considered as the final result.)

Hence, the value of xy is (a²+b²)