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

To perform basic operations with complex numbers z1=(3+2i) and z2=(2-i), we can follow the following steps:

1. Addition: To add z1 and z2, we add the real parts and imaginary parts separately. z1 + z2 = (3 + 2i) + (2 - i) = (3 + 2) + (2i - i) = 5 + i

2. Subtraction: To subtract z2 from z1, we subtract the real parts and imaginary parts separately. z1 - z2 = (3 + 2i) - (2 - i) = (3 - 2) + (2i + i) = 1 + 3i

3. Multiplication: To multiply z1 and z2, we use the FOIL method. z1 * z2 = (3 + 2i) * (2 - i) = 32 + 3(-i) + 2i2 + 2i(-i) = 6 - 3i + 4i - 2i^2 = 6 + i + 4i - 2*(-1) = 6 + i + 4i + 2 = 8 + 5i

4. Division: To divide z1 by z2, we multiply both the numerator and denominator by the conjugate of the denominator. z1 / z2 = (3 + 2i) / (2 - i) = (3 + 2i) * (2 + i) / (2 - i) * (2 + i) = (6 + 3i + 4i + 2i^2) / (4 + 2i - 2i - i^2) (i^2 = -1) = (6 + 7i - 2) / (4 + 1) = 4 + 7i / 5

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