(3i)(-2+4i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (3i)(-2 + 4i)

This article will guide you through the process of multiplying two complex numbers: (3i)(-2 + 4i).

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 (i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property:

1. Distribute: Multiply each term inside the parentheses by the factor outside: (3i)(-2 + 4i) = (3i)(-2) + (3i)(4i)

2. Simplify: Multiply the real and imaginary parts separately: = -6i + 12i²

3. Substitute i²: Remember that i² = -1. Substitute this value: = -6i + 12(-1)

4. Combine terms: Combine the real and imaginary terms: = -12 - 6i

Final Result

Therefore, the product of (3i)(-2 + 4i) is -12 - 6i.