9i / -3+8i
5i
9i/(-3+8i) = (9i)(-3-8i)/(3^2+8^2) = (72-27i)/73
To divide complex numbers, we can use the formula for dividing complex numbers in the form a+bi:
(a + bi) / (c + di) = [(a * c) + (b * d)] / (c^2 + d^2) + [(b * c) - (a * d)i] / (c^2 + d^2)i
Let's apply this formula to the expression 9i / (-3 + 8i):
a = 0 (since there is no real part in 9i)
b = 9 (the imaginary part in 9i)
c = -3 (the real part in -3 + 8i)
d = 8 (the imaginary part in -3 + 8i)
Now, we substitute these values into the formula:
[(0 * -3) + (9 * 8)] / ((-3)^2 + 8^2) + [(9 * -3) - (0 * 8)i] / ((-3)^2 + 8^2)i
Simplifying this expression, we get:
(72 / 73) + (-27 / 73)i
So, the division of 9i by -3 + 8i is equal to (72 / 73) + (-27 / 73)i.