Question

Which complex number is the simplified form of 2+5i3+i2+5i3+i?

Answer 1

Answer:

Option (1)

Step-by-step explanation:

The given complex  number is (2+5i)/(3+i)

multiplying the numerator and the denominator by the conjugate of (3+i) which is (3-i)

The denominator = (3+i)(3-i) = 3² - i² = 9 - (-1) = 10

The numerator  = (2 + 5 i ) ( 3 - i ) = 2(3-i) + 5i (3 - i)

                          = 6 - 2i + 15 i - 5 i²

                          = 6 + 13 i + 5 = 11 + 13 i

So, the given complex number can be simplified to ( 11 + 13i)/10

Distributing numerator over denominator.

The simplified  number = (11/10) + (13/10) i

The answer is option (1)