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)
