(2i)(6+3i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (2i)(6+3i)

This article will guide you through the process of simplifying the complex number expression (2i)(6 + 3i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where:

• a is the real part of the number.
• b is the imaginary part of the number.
• i is the imaginary unit, defined as the square root of -1 (i² = -1).

Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property (also known as FOIL):

(2i)(6 + 3i) = (2i * 6) + (2i * 3i)

Simplifying the Expression

1. Distribute: (2i * 6) + (2i * 3i) = 12i + 6i²

2. Substitute i² with -1: 12i + 6i² = 12i + 6(-1)

3. Combine terms: 12i + 6(-1) = -6 + 12i

The Final Answer

Therefore, the simplified form of (2i)(6 + 3i) is -6 + 12i. This expression represents a complex number with a real part of -6 and an imaginary part of 12.