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

To prepare for your university exams, it is important to understand the basic operations involving complex numbers. Let's go through the given complex numbers and perform the requested calculations.

1. z1 = (12 - i) The given complex number is already in the standard form, where the real part is 12 and the imaginary part is -1.

2. z2 = (-1 - i) Similar to the first one, this complex number is already in standard form, where the real part is -1 and the imaginary part is -1.

3. z3 = (4 + 3i) Once again, this is already in the standard form, with the real part being 4 and the imaginary part being 3.

4. z4 = (-3 - 2i) Just like the previous complex numbers, this one is already in the standard form, with the real part being -3 and the imaginary part being -2.

Now, let's perform some basic operations involving these complex numbers.

Addition: To add complex numbers, you simply add their corresponding real and imaginary parts. z1 + z2 = (12 - i) + (-1 - i) = 12 - 1 + (-i - i) = 11 - 2i

Subtraction: To subtract complex numbers, you subtract their corresponding real and imaginary parts. z1 - z2 = (12 - i) - (-1 - i) = 12 - (-1) + (-i - (-i)) = 12 + 1 + 0 = 13

Multiplication: To multiply complex numbers, you can use the distributive property or FOIL method. z1 * z3 = (12 - i) * (4 + 3i) = 12 * 4 + 12 * 3i - i * 4 - i * 3i = 48 + 36i - 4i - 3i^2 (remember that i^2 = -1) = 48 + 36i - 4i + 3 = 51 + 32i

Division: To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator, and then simplify. z2 / z4 = (-1 - i) / (-3 - 2i) = (-1 - i) * (-3 + 2i) / (-3 - 2i) * (-3 + 2i) = (-1 * -3) + (-1 * 2i) + (-i * -3) + (-i * 2i) / (-3 * -3) + (-3 * 2i) + (-2i * -3) + (-2i * 2i) = 3 - 2i + 3i + 2i^2 / 9 - 6i - 6i + 4i^2 = 3 - 2i + 3i + 2(-1) / 9 - 6i - 6i + 4(-1) = 3 + i - 2 / 9 - 12i - 4 = 1 + i / 5 - 12i

I hope this helps with your exam preparation! If you have any more questions, feel free to ask. Good luck!