(−3+2i)(1−i3)

Jasonbradley

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Jun 17, 2024

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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):

1. First: (−3)(1) = -3
2. Outer: (−3)(−i3) = 9i
3. Inner: (2i)(1) = 2i
4. 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.