Z1=(8-7i) z2=(-4+7i)

To perform calculations with complex numbers, we use the following operations:

1. Addition: To add complex numbers, we add the real parts and the imaginary parts separately.

   (z1 + z2) = (8 - 7i) + (-4 + 7i) = (8 - 4) + (-7 + 7)i = 4 + 0i = 4

2. Subtraction: To subtract complex numbers, we subtract the real parts and the imaginary parts separately.

   (z1 - z2) = (8 - 7i) - (-4 + 7i) = (8 + 4) + (-7 - 7)i = 12 - 14i

3. Multiplication: To multiply complex numbers, we use the FOIL method and remember that i^2 is equal to -1.

   (z1 * z2) = (8 - 7i) * (-4 + 7i) = (8 * -4) + (8 * 7i) + (-7i * -4) + (-7i * 7i) = -32 + 56i + 28i - 49i^2 = -32 + 84i + 49 = 17 + 84i

4. Division: To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator.

   (z1 / z2) = (8 - 7i) / (-4 + 7i) = [(8 - 7i) / (-4 + 7i)] * [(-4 - 7i) / (-4 - 7i)] = ([(8 * -4) + (8 * -7i) - (7i * -4) - (7i * -7i)]) / [(4 * 4) - (7i * 7i)] = (-32 - 56i + 28i + 49) / (16 + 49) = (-32 - 28i + 49 + 28i) / 65 = 17 / 65 + 0i

Therefore,

1. (z1 + z2) = 4
2. (z1 - z2) = 12 - 14i
3. (z1 * z2) = 17 + 84i
4. (z1 / z2) = 17 / 65 + 0i