Question 1194519
**1. Analytical Solutions**

**(a) Z1 - Z2 + Z3**

* Z1 - Z2 + Z3 = (2 - 2i) - 3i + (-3 + i) 
* Z1 - Z2 + Z3 = 2 - 2i - 3i - 3 + i 
* Z1 - Z2 + Z3 = -1 - 4i

**(b) Z3 - Z2 - Z1**

* Z3 - Z2 - Z1 = (-3 + i) - 3i - (2 - 2i) 
* Z3 - Z2 - Z1 = -3 + i - 3i - 2 + 2i 
* Z3 - Z2 - Z1 = -5 

**2. Graphical Illustration**

* **Represent complex numbers as vectors:**
    * Z1 = 2 - 2i: Vector from origin to point (2, -2) in the complex plane.
    * Z2 = 3i: Vector from origin to point (0, 3) in the complex plane.
    * Z3 = -3 + i: Vector from origin to point (-3, 1) in the complex plane.

* **Perform vector operations graphically:**
    * **(a) Z1 - Z2 + Z3:** 
        * Draw Z1. 
        * Draw -Z2 (vector Z2 in the opposite direction). 
        * Draw Z3.
        * The vector sum Z1 - Z2 + Z3 is the resultant vector obtained by connecting the tail of Z1 to the head of Z3 after drawing -Z2. 

    * **(b) Z3 - Z2 - Z1:**
        * Draw Z3.
        * Draw -Z2.
        * Draw -Z1 (vector Z1 in the opposite direction).
        * The vector sum Z3 - Z2 - Z1 is the resultant vector obtained by connecting the tail of Z3 to the head of -Z1 after drawing -Z2.

**3. Further Calculations**

**(c) Z1 * Z3**

* Z1 * Z3 = (2 - 2i) * (-3 + i) 
* Z1 * Z3 = -6 + 2i + 6i - 2i² 
* Z1 * Z3 = -6 + 8i + 2 (since i² = -1)
* Z1 * Z3 = -4 + 8i

**(d) Z3 x Z2**

* The cross product is not defined for complex numbers in the same way it is for vectors in 3D space. 

**(e) Acute Angle between Z1 and Z2**

* Find the magnitudes of Z1 and Z2:
    * |Z1| = √(2² + (-2)²) = √8 = 2√2
    * |Z2| = √(0² + 3²) = 3

* Find the dot product of Z1 and Z2:
    * Z1 • Z2 = (2 * 0) + (-2 * 3) = -6

* Use the dot product formula:
    * cos(θ) = (Z1 • Z2) / (|Z1| * |Z2|)
    * cos(θ) = -6 / (2√2 * 3) 
    * cos(θ) = -√2 / 2
    * θ = 135° 

* The acute angle between Z1 and Z2 is 180° - 135° = 45°.

**Note:**

* Graphical representation can be done using a complex plane (Argand diagram). 
* You can use graphing software or tools to plot the complex numbers and visualize the vector operations.

I hope this comprehensive explanation helps!