Question

What is the value of 15i/ 2 + i

Answer 1

Answer:

The value of the given expression is $\frac{15i}{2+i}=3(2i+1)$

Step-by-step explanation:

Given : Expression $\frac{15i}{2+i}$

To find : The value of the given expression?

Solution :          

We solve the expression by rationalizing,

$\frac{15i}{2+i}$

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

$=\frac{15i}{2+i}\times \frac{2-i}{2-i}$

$=\frac{15i(2-i)}{(2+i)(2-i)}$

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

$=\frac{30i-15i^2}{2^2-i^2}$

We know, $i^2=-1$

$=\frac{30i-15(-1)}{2^2-(-1)}$

$=\frac{30i+15}{4+1}$

$=\frac{30i+15}{5}$

Divide by 5,

$=6i+3$

$=3(2i+1)$

Therefore, The value of the given expression is $\frac{15i}{2+i}=3(2i+1)$

Answer 2

the answer would be

3 + 6i