(5i)(3+4i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (5i)(3 + 4i)

This article will guide you through the process of multiplying the complex numbers (5i) and (3 + 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 term outside the parentheses.

   • (5i)(3 + 4i) = (5i)(3) + (5i)(4i)

2. Simplify:

   • (5i)(3) = 15i
   • (5i)(4i) = 20i²

3. Substitute i² = -1:

   • 20i² = 20(-1) = -20

4. Combine Real and Imaginary Terms:

   • 15i - 20 = -20 + 15i

Result

Therefore, the product of (5i) and (3 + 4i) is -20 + 15i.