## Multiplying Complex Numbers: (−3+2i)(1−i3)

This article will guide you through the process of multiplying complex numbers. We'll focus on the specific example of **(−3+2i)(1−i3)**.

### Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form **a + bi**, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as the square root of -1.

### Multiplying Complex Numbers

When multiplying complex numbers, we use the distributive property (often referred to as FOIL - First, Outer, Inner, Last) similar to multiplying binomials.

Let's break down the multiplication of **(−3+2i)(1−i3)**:

**First:**(−3)(1) =**-3****Outer:**(−3)(−i3) =**9i****Inner:**(2i)(1) =**2i****Last:**(2i)(−i3) =**−6i²**

Now, remember that **i² = -1**. Substitute this into our result:

-3 + 9i + 2i - 6(-1)

Combining like terms:

-3 + 9i + 2i + 6 = **3 + 11i**

### Final Result

Therefore, the product of **(−3+2i)(1−i3)** is **3 + 11i**.