Simplify: (8-6i)/ 3i:
A. 6
B. (6 + 8i)/ -3
C. (6 + 8i)/ 3
D. 2 + 8i
To simplify the given expression, (8-6i) / 3i, we can use the following steps:
Step 1: Multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of 3i is -3i. So, we have:
(8 - 6i) / 3i * (-3i / -3i)
Step 2: Simplify the numerator and denominator.
Multiplying the numerators and denominators gives us:
(-24i + 18i^2) / (-9i^2)
Step 3: Simplify the numbers with exponents.
Since i^2 is equal to -1, we can substitute the value into the expression:
(-24i + 18(-1)) / (-9(-1))
Step 4: Perform the calculations.
(-24i - 18) / 9
Step 5: Divide both terms separately.
-24i / 9 - 18 / 9
Step 6: Simplify the results.
- (8/3)i - 2
Therefore, the simplified form of (8-6i) / 3i is:
- (8/3)i - 2
So, the correct answer is option C: (6 + 8i) / 3.