Answer:
The value of the given expression is [tex]\frac{15i}{2+i}=3(2i+1)[/tex]
Step-by-step explanation:
Given : Expression [tex]\frac{15i}{2+i}[/tex]
To find : The value of the given expression?
Solution :
We solve the expression by rationalizing,
[tex]\frac{15i}{2+i}[/tex]
Rationalize by multiplying the Nr. and Dr. by 2-i
[tex]=\frac{15i}{2+i}\times \frac{2-i}{2-i}[/tex]
[tex]=\frac{15i(2-i)}{(2+i)(2-i)}[/tex]
Applying property, [tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]=\frac{30i-15i^2}{2^2-i^2}[/tex]
We know, [tex]i^2=-1[/tex]
[tex]=\frac{30i-15(-1)}{2^2-(-1)}[/tex]
[tex]=\frac{30i+15}{4+1}[/tex]
[tex]=\frac{30i+15}{5}[/tex]
Divide by 5,
[tex]=6i+3[/tex]
[tex]=3(2i+1)[/tex]
Therefore, The value of the given expression is [tex]\frac{15i}{2+i}=3(2i+1)[/tex]
