(6+2i)(3i)

2 min read Jun 16, 2024
(6+2i)(3i)

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

This article explores the multiplication of complex numbers, specifically the expression (6 + 2i)(3i).

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, just like we would with any binomial multiplication.

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

  2. Simplify: = 18i + 6i²

  3. Substitute i² = -1: = 18i + 6(-1)

  4. Combine Real and Imaginary Terms: = -6 + 18i

Result

Therefore, the product of (6 + 2i) and (3i) is -6 + 18i.

Key Points

  • Complex number multiplication involves multiplying both the real and imaginary components of the numbers.
  • The distributive property is essential in simplifying these multiplications.
  • Remember that i² = -1.

This example demonstrates a straightforward approach to multiplying complex numbers. It's a fundamental operation in various mathematical applications, particularly in areas like electrical engineering and quantum mechanics.

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