Z1=(6-i) z2=(-3-3i)

To perform calculations with complex numbers z1 and z2, we can use the following operations:

1. Addition: To add complex numbers, add the real parts and the imaginary parts separately. For z1 + z2: z1 + z2 = (6 - i) + (-3 - 3i) = (6 + (-3)) + (-1 - 3)i = 3 - 4i

2. Subtraction: To subtract complex numbers, subtract the real parts and the imaginary parts separately. For z1 - z2: z1 - z2 = (6 - i) - (-3 - 3i) = (6 - (-3)) + (-1 - (-3))i = 9 + 2i

3. Multiplication: To multiply complex numbers, use FOIL method, considering that i^2 = -1. For z1 * z2: z1 * z2 = (6 - i) * (-3 - 3i) = -18 - 18i + 3i + 3i^2 = -18 - 15i + 3i^2 = -18 - 15i + 3(-1) = -18 - 15i - 3 = -21 - 15i

4. Division: To divide complex numbers, multiply both numerator and denominator by the complex conjugate of the denominator. For z1 / z2: z1 / z2 = (6 - i) / (-3 - 3i) = (6 - i) * (-3 + 3i) / (-3 - 3i) * (-3 + 3i) = (-18 + 18i + 3i - 3i^2) / (9 - 9i + 9i - 9i^2) = (-18 + 21i - 3) / (9 + 9) = (-21 + 21i) / 18 = -7/6 + 7i/6

These are the operations that can be performed with complex numbers z1 and z2.