Question

Find the product of these, then find the total mean of all five products.
(2,-2)
(2,-7)
(3,7)
(-4,-1)
(-6,-2)

Answer 1

To find the product of two complex numbers, we simply multiply their corresponding terms and combine them. Thus, the product of (2,-2) and (2,-7) would be:

(2,-2) * (2,-7) = (2*2 - (-2)*(-7), 2*(-7) + 2*(-2)) = (4 - 14, -14 - 4) = (-10, -18)

Similarly, we can find the products of the other pairs:

(2,-2) * (3,7) = (2*3 - (-2)*7, 2*7 + 2*3) = (6 + 14, 14 + 6) = (20, 20)

(2,-2) * (-4,-1) = (2*(-4) - (-2)*(-1), 2*(-1) + (-2)*(-4)) = (-8 + 2, -2 + 8) = (-6, 6)

(2,-2) * (-6,-2) = (2*(-6) - (-2)*(-2), 2*(-2) + (-2)*(-6)) = (-12 - 4, -4 - 12) = (-16, -16)

Finally, we find the mean of all five products:

(-10 - 18 + 20 + (-6) + (-16)) / 5 = (-30) / 5 = -6

So, the total mean of all five products is -6.