Could someone help me check my answer? Thanks.
-Write each quotient as a complex number.
1. 3i/-2+i
(Is the answer for this one = 3/5-6i/5)
3i/(-2+i)
= 3i/(-2+i) * (-2-i)/(-2-i)
=(-6i - 3i^2)/4 - i^2)
= (3 - 6i)/5
yes you are correct
To write the quotient 3i / (-2 + i) as a complex number, we need to rationalize the denominator. We can do this by multiplying both the numerator and the denominator by the conjugate of the denominator, which in this case is (-2 - i).
First, let's multiply the numerator and denominator by the conjugate:
(3i / -2 + i) * (-2 - i / -2 - i)
Multiplying the numerator and denominator out, we get:
(3i * -2 - 3i^2) / (-2 * -2 - 2 * i + 2 * i - i^2)
Simplifying further:
(-6i + 3) / (4 + 1)
Now, we can write this as a complex number:
(-6i + 3) / 5
So, the correct answer is:
(3/5) - (6i/5)
To check your answer, we need to simplify the expression 3i / (-2 + i) and see if it matches the result you've provided (3/5 - 6i/5).
To simplify this complex division, we need to multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of -2 + i is -2 - i.
1. Multiply the numerator and denominator by the conjugate:
(3i / (-2 + i)) * (-2 - i) / (-2 - i)
By doing this, we eliminate the imaginary part in the denominator.
2. Simplify the expression:
(3i * (-2 - i)) / (-2 * -2 - i * -2 + i * -2 + i * i)
Multiply the terms:
(-6i - 3i^2) / (4 + 2i - 2i - i^2)
Since i^2 = -1, we can simplify further:
(-6i - 3(-1)) / (4 - (-1))
(-6i + 3) / 5
So, the simplified expression is (3 - 6i) / 5, not 3/5 - 6i/5.
Please double-check your calculations.