Question

Evaluate (5 - 2i)/(7 - i).

Options:
a) (37/50) - (9/50)i
b) (37 - 9i)/50
c) (5/7) - (2/7)i
d) (50 - 37i)/50

Answer 1

To evaluate the expression (5 - 2i)/(7 - i), multiply the numerator and denominator by the conjugate of the denominator and simplify the expression.

Step-by-step explanation:

To evaluate the expression (5 - 2i)/(7 - i):

1. First, multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of 7 - i is 7 + i.
2. This gives us (5 - 2i)(7 + i) / (7 - i)(7 + i).
3. Expanding and simplifying, we get (35 + 5i - 14i - 2i^2) / (49 - i^2).
4. Since i^2 is equal to -1, the expression simplifies to (33 - 9i) / 50.
5. Therefore, the correct answer is option b) (37 - 9i)/50.