Z1=(12+5i) z2=(3-4 i)

To perform the required operations, we can apply basic algebraic operations on complex numbers.

1. Addition: To add the two complex numbers z1 and z2, we simply add their real parts and their imaginary parts separately: z1 + z2 = (12 + 5i) + (3 - 4i) = (12 + 3) + (5 - 4)i = 15 + i

2. Subtraction: To subtract z2 from z1, we subtract their real parts and their imaginary parts separately: z1 - z2 = (12 + 5i) - (3 - 4i) = (12 - 3) + (5 + 4)i = 9 + 9i

3. Multiplication: To multiply z1 and z2, we can use the distributive property and multiply each term separately: z1 * z2 = (12 + 5i) * (3 - 4i) = 123 + 12(-4i) + 5i3 + 5i(-4i) = 36 - 48i + 15i - 20i^2 = 36 - 48i + 15i + 20 = 56 - 33i

4. Division: To divide z1 by z2, we multiply the numerator and denominator by the conjugate of z2, which is the same complex number with the opposite sign in the imaginary part: z1 / z2 = (12 + 5i) / (3 - 4i) = (12 + 5i) * (3 + 4i) / (3 - 4i) * (3 + 4i) = (123 + 124i + 5i3 + 5i4i) / (3^2 - (4i)^2) = (36 + 48i + 15i + 20i^2) / (9 + 16) = (56 + 63i) / 25 = (56/25) + (63/25)i

Therefore, the results of the operations are:

1. Addition: 15 + i
2. Subtraction: 9 + 9i
3. Multiplication: 56 - 33i
4. Division: (56/25) + (63/25)i