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

To prepare for university exams, it is important to understand the basic operations on complex numbers.

First, let's understand the basic operations on complex numbers:

1. Addition: To add two complex numbers, we add their real parts and their imaginary parts separately. For example, to add z1 and z2, we add their real parts (3+2) and (2) to get the new real part, and their imaginary parts (2i) and (-i) to get the new imaginary part. The sum of z1 and z2 is: (3+2) + (2) + (2i + (-i)) = 5 + i.

2. Subtraction: Similar to addition, to subtract two complex numbers, we subtract their real parts and their imaginary parts separately. For example, to subtract z2 from z1, we subtract their real parts (3-2) and (2) to get the new real part, and their imaginary parts (2i) and (-i) to get the new imaginary part. The subtraction of z2 from z1 is: (3-2) - (2) + (2i - (-i)) = 1 + 3i.

3. Multiplication: To multiply two complex numbers, we can use the distributive property or the FOIL method. For example, to multiply z1 and z2, we can use the FOIL method: (3 + 2i) * (2 - i) = 6 - 3i + 4i - 2i^2. Simplifying this further, we get: 6 + i + 2 = 8 + i.

4. Division: To divide two complex numbers, we multiply the numerator and the denominator by the conjugate of the denominator. For example, to divide z1 by z2, we have: (3 + 2i) / (2 - i). We multiply the numerator and the denominator by the conjugate of the denominator, which is (2 + i). Simplifying this further, we get: [(3 + 2i) * (2 + i)] / [(2 - i) * (2 + i)] = (6 + 3i + 4i + 2i^2) / (4 + 2i - 2i - i^2). Simplifying this further, we get: (6 + 7i - 2) / (4 + 1) = 4 + 7i.

These are the basic operations on complex numbers. Make sure to practice these operations and understand their properties to prepare for university exams.