Z1=(5-2i) z2=(3-3i)

To prepare for the exams, you'll need to understand and practice various operations with complex numbers. Here are some common operations you can perform with the given complex numbers:

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

   z1 + z2 = (5-2i) + (3-3i) = (5 + 3) + (-2 - 3)i = 8 - 5i

2. Subtraction: Similar to addition, subtract the real parts and the imaginary parts individually.

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

3. Multiplication: Multiply complex numbers by distributing each term. Remember that i^2 = -1.

   z1 * z2 = (5-2i) * (3-3i) = (5 * 3) + (5 * -3i) + (-2i * 3) + (-2i * -3i) = 15 - 15i - 6i + 6i^2 = 15 - 21i - 6i + 6(-1) = 15 - 21i - 6i - 6 = 9 - 27i

4. Division: Divide complex numbers by multiplying both the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.

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

Make sure to understand these operations and practice solving similar problems to improve your preparation for the exams.