Question

Rewrite the expression in (a + bi) form: 7−9i/6i

A) (1.5 - 1.5i)
B) (-1.5 + 1.5i)
C) (-1.5 - 1.5i)
D) (1.5 + 1.5i)

Answer 1

To rewrite the expression (7−9i/6i) in (a + bi) form, multiply the numerator and denominator by the complex conjugate of the denominator, which in this case is −6i. After simplification, the expression is (−1.5 − 1.5i), corresponding to option C.

Step-by-step explanation:

To rewrite the expression 7−9i/6i in (a + bi) form, we need to eliminate the complex number in the denominator. We can do this by multiplying both the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of 6i is −6i.

First, multiply the numerator and denominator:

(7 − 9i) * (−6i) / (6i * (−6i)) =
(7 * (−6i)) + (9i * (−6i)) / 36 =
(−42i − 54) / 36

Now, we simplify by dividing each term by 36:

(−42i)/36 = −1.5i
(−54)/36 = −1.5

Therefore, the expression in (a + bi) form is (−1.5 − 1.5i), which matches option C.