Solve (-2+i) / (3-2i) and my answer is (-8-i) / 13.
Correct?
yes, and it is 0.6202∠-172.87 in polar form
I get (-4 - i)/13
(-2+i) / (3-2i)
= (-2+i) / (3-2i) * (3+2i)/(3+2i)
= (-6-4i + 3i - 2i^2)/(9 - 4i^2)
= (-6 - i + 2)/(9+4)
= ( -4 - i)/13
To solve the fraction (-2+i) / (3-2i), we can use a method called rationalizing the denominator. Rationalizing the denominator means getting rid of any imaginary numbers in the denominator.
To do this, we multiply both the numerator and the denominator by the conjugate of the denominator, which is found by changing the sign of the imaginary part. In this case, the conjugate of 3-2i is 3+2i.
So, let's multiply the numerator and the denominator by 3+2i:
((-2+i) * (3+2i)) / ((3-2i) * (3+2i))
Expanding the numerator and the denominator, we get:
(-6 - 4i + 3i - 2) / (9 + 6i - 6i - 4i^2)
Simplifying further:
(-8 - i) / (9 + 4)
Since i^2 is equal to -1, we have:
(-8 - i) / 13
Therefore, your answer of (-8 - i) / 13 is correct.