Multiplying Complex Numbers: (4 + 4i) * (3 + 2i)
This article will guide you through multiplying the complex numbers (4 + 4i) and (3 + 2i).
Understanding Complex Numbers
Before diving into the multiplication, let's quickly recap complex numbers. Complex numbers are expressed in the form a + bi, where:
 a is the real part.
 b is the imaginary part.
 i is the imaginary unit, where i² = 1.
Multiplication Process
To multiply complex numbers, we use the distributive property, similar to multiplying binomials.

Expand the product: (4 + 4i) * (3 + 2i) = (4 * 3) + (4 * 2i) + (4i * 3) + (4i * 2i)

Simplify the terms: = 12  8i + 12i + 8i²

Substitute i² with 1: = 12  8i + 12i + 8(1)

Combine real and imaginary terms: = (12  8) + (8 + 12)i

Final Result: = 20 + 4i
Therefore, the product of (4 + 4i) and (3 + 2i) is 20 + 4i.
Visual Representation
You can visualize this multiplication on the complex plane. Each complex number corresponds to a point on the plane. Multiplying complex numbers can be thought of as a rotation and scaling operation on the complex plane.
Applications
Complex numbers have numerous applications in various fields, including:
 Engineering: Electrical circuits, signal processing, control systems
 Physics: Quantum mechanics, wave phenomena
 Mathematics: Solving equations, representing geometric transformations
Understanding complex number multiplication is essential for working with these applications.