z1=(5-2i) z2=(3-3i)

To perform arithmetic operations on complex numbers z1 and z2, follow these steps:

1. Addition: z1 + z2 = (5 - 2i) + (3 - 3i) = 5 + 3 - 2i - 3i = 8 - 5i

Therefore, z1 + z2 = 8 - 5i.

2. Subtraction: z1 - z2 = (5 - 2i) - (3 - 3i) = 5 - 3 - 2i + 3i = 2 + i

Therefore, z1 - z2 = 2 + i.

3. Multiplication: z1 * z2 = (5 - 2i) * (3 - 3i) = (5 * 3) + (5 * -3i) + (-2i * 3) + (-2i * -3i) = 15 - 15i - 6i + 6i² = 15 - 21i + 6(-1) = 15 - 21i - 6 = 9 - 21i

Therefore, z1 * z2 = 9 - 21i.

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

z1 / z2 = ((5 - 2i) * (3 + 3i)) / ((3 - 3i) * (3 + 3i)) = ((5 * 3) + (5 * 3i) + (-2i * 3) + (-2i * 3i)) / (3 * 3 + 3 * -3i + -3i * 3 + -3i * -3i) = (15 + 15i - 6i - 6i²) / (9 + -9i - 9i + 9i²) = (15 + 15i - 6i + 6) / (9 + 9i - 9i + 9) = (21 + 9i) / (18) = (21/18) + (9i/18) = (7/6) + (1/2)i

Therefore, z1 / z2 = (7/6) + (1/2)i.