Respuesta :
3 + 6i
multiply the numerator/ denominator by the conjugate of 2 + i
the conjugate of 2 + i = 2 - i
[tex]\frac{15(2-i)}{(2+i)(2-i)}[/tex]
= ( 30i - 15i² ) / (4 - i² ) → ( i² = (√-1 )² = -1 )
= [tex]\frac{30i+15}{5}[/tex] = 6i + 3
Answer:
3+6i
Step-by-step explanation:
[tex]\frac{15i}{2+i}[/tex]
To divide we multiply by the conjugate of denominator
conjugate of 2+i is 2-i
Multiply top and bottom by 2-i
[tex]\frac{(15i)(2-i)}{(2+i)(2-i)}[/tex]
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
[tex]\frac{30i+15)}{5}[/tex]
Divide each term by 5
6i+3
so its 3+6i
