Z1=(12-i) z2=(-1- i) z3(4+3i) z4(-3-2 I)

To perform arithmetic operations on complex numbers, we can use the following guidelines:

• Addition: To add two complex numbers, add their real parts and their imaginary parts separately. For example: z1 + z2 = (12 - i) + (-1 - i) = 12 - i - 1 - i = 11 - 2i

• Subtraction: To subtract two complex numbers, subtract their real parts and their imaginary parts separately. For example: z2 - z3 = (-1 - i) - (4 + 3i) = -1 - 4 - i - 3i = -5 - 4i - 3i = -5 - 7i

• Multiplication: To multiply two complex numbers, distribute and combine like terms. Remember, i^2 = -1. For example: z3 * z4 = (4 + 3i) * (-3 - 2i) = -12 - 8i - 9i - 6i^2 = -12 - 17i - 6(-1) = -12 - 17i + 6 = -6 - 17i

• Division: To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example: z1 / z2 = (12 - i) / (-1 - i) = (12 - i)(-1 + i) / (-1 - i)(-1 + i) = (-12 + 12i + i - i^2) / (1^2 - i^2) = (-12 + 13i + 1) / (1 + 1) = (-11 + 13i) / 2 = -11/2 + 13/2 i

I hope this helps! Let me know if you have any further questions.