Question 488110
Hey,
So for this problem we need to do what is called Foiling, which is a special way of solving these types of problems, which are called polynomials.
So first we multiply the first variable in each parentheses:
(-4+6i)(-3+7i) => -4 x -3 = 12
Then the first variable in the first parentheses is multiplied by the second variable in the second parentheses:
(-4+6i)(-3+7i) => -4 x 7i = -28i
Then the second variable in the first parentheses is multiplied by the first variable in the second parentheses:
(-4+6i)(-3+7i) => 6i x -3 = -18i
Finally the second variable in the first parentheses is multiplied by the second variable in the second parentheses:
(-4+6i)(-3+7i) => 6i x 7i = 42(i^2). Now when i is squared it becomes -1, so the result is actually -42.
Now we add all of the results that we got from foiling:
12 + (-28i) + (-18i) + (-42) = -30 - 46i 
So the answer is -30 - 46i
I hope this helps!