Question

What is the value of 15i/ 2 + i

Answer 1

the answer would be

3 + 6i

Answer 2

The value of the given expression is
`(15i)/(2+i)=3(2i+1)`

Explanation:

Given : Expression
`(15i)/(2+i)`

To find : The value of the given expression?

Solution :

We solve the expression by rationalizing,

`(15i)/(2+i)`

Rationalize by multiplying the Nr. and Dr. by 2-i

`=(15i)/(2+i)* (2-i)/(2-i)`

`=(15i(2-i))/((2+i)(2-i))`

Applying property,
`(a+b)(a-b)=a^2-b^2`

`=(30i-15i^2)/(2^2-i^2)`

We know,
`i^2=-1`

`=(30i-15(-1))/(2^2-(-1))`

`=(30i+15)/(4+1)`

`=(30i+15)/(5)`

Divide by 5,

`=6i+3`

`=3(2i+1)`

Therefore, The value of the given expression is
`(15i)/(2+i)=3(2i+1)`