Question

1/(-8 - 5i) simplifies to:
A) -1/13
B) 1/13
C) -1/5i
D) 1/5i

Answer 1

To simplify the expression 1/(-8 - 5i), multiply the numerator and denominator by the conjugate of the denominator and then simplify.

Step-by-step explanation:

To simplify the expression 1/(-8 - 5i), we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of -8 - 5i is -8 + 5i. Therefore, the expression becomes:

1/(-8 - 5i) × (-8 + 5i)/(-8 + 5i) = (-8 + 5i)/((-8)(-8) + (-8)(5i) + (5i)(-8) + (5i)(5i))

Simplifying the denominator: 64 + 40i - 40i - 25 = 39

So, the simplified expression is:

(-8 + 5i)/39