Question

What is the value of 15i/2+i ?
–3 + 6i
3 + 6i
5 + 5i
5 – 5i

Answer 1

3 + 6i

multiply the numerator/ denominator by the conjugate of 2 + i

the conjugate of 2 + i = 2 - i

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

= ( 30i - 15i² ) / (4 - i² ) → ( i² = (√-1 )² = -1 )

=
`(30i+15)/(5)` = 6i + 3

Answer 2

3+6i

Explanation:

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

To divide we multiply by the conjugate of denominator

conjugate of 2+i is 2-i

Multiply top and bottom by 2-i

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

Apply FOIL method to multiply. value of i^2 = -1

(15i)(2-i) = 30i - 15i^2 = 30i +15(-1)= 30i+15

(2+i)(2-i)= 4 - i^2 = 4+1= 5

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

Divide each term by 5

6i+3

so its 3+6i