4.

a)

b)

c)

If |z1|=8 and |z2|=3 then maximum value of |z1-zz| is

5

11

24

To find the maximum value of |z1 - z2| given |z1| = 8 and |z2| = 3, we can use the triangle inequality. The triangle inequality states that for any complex numbers z1 and z2, the following holds:

Triangle Inequality

|z1 - z2| ≤ |z1| + |z2|

|z1 - z2| ≥ ||z1| - |z2||

Calculating the Maximum Value

Using the values provided:

• |z1| = 8
• |z2| = 3

Applying the triangle inequality:

• Maximum: |z1| + |z2| = 8 + 3 = 11
• Minimum: ||z1| - |z2|| = |8 - 3| = 5

Conclusion

The maximum value of |z1 - z2| is 11, and the minimum value is 5. Therefore, the answer to your question is:

11