Z1=(-1+2i) z2=(5-5i)

To perform operations between complex numbers, we can use the following rules:

1. Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
2. Subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i
3. Multiplication: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
4. Division: (a + bi) / (c + di) = [(ac + bd) / (c^2 + d^2)] + [(bc - ad) / (c^2 + d^2)]i

Now, let's perform the given operations:

1. Addition: z1 + z2 = (-1 + 2i) + (5 - 5i) = (-1 + 5) + (2 - 5)i = 4 - 3i

2. Subtraction: z1 - z2 = (-1 + 2i) - (5 - 5i) = (-1 - 5) + (2 + 5)i = -6 + 7i

3. Multiplication: z1 * z2 = (-1 + 2i) * (5 - 5i) = (-1 * 5 - 2 * (-5)) + (-1 * (-5) + 2 * 5)i = (-5 + 10) + (5 + 10)i = 5 + 15i

4. Division: z1 / z2 = (-1 + 2i) / (5 - 5i) = [(-1 * 5 + 2 * 5) / (5^2 + (-5)^2)] + [(2 * 5 + (-1) * (-5)) / (5^2 + (-5)^2)]i = (5 + 15) / (25 + 25) + (10 + 5) / (25 + 25)i = 20/50 + 15/50i = 2/5 + 3/10i

Therefore, the results of the given operations are:

1. Addition: z1 + z2 = 4 - 3i
2. Subtraction: z1 - z2 = -6 + 7i
3. Multiplication: z1 * z2 = 5 + 15i
4. Division: z1 / z2 = 2/5 + 3/10i