(3i)(2i)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (3i)(2i)^2

This article aims to explain how to simplify the expression (3i)(2i)^2.

Understanding the Concepts

• Imaginary Unit (i): The imaginary unit i is defined as the square root of -1, i.e., √(-1) = i.
• Powers of i: The powers of i follow a cyclical pattern:
  • i^1 = i
  • i^2 = -1
  • i^3 = -i
  • i^4 = 1
• Multiplication of Complex Numbers: Complex numbers are multiplied similarly to binomial multiplication, remembering that i^2 = -1.

Simplifying the Expression

1. Simplify the exponent: (2i)^2 = (2i)(2i) = 4i^2

2. Substitute i^2 with -1: 4i^2 = 4(-1) = -4

3. Multiply with the remaining term: (3i)(-4) = -12i

Final Answer

Therefore, the simplified form of (3i)(2i)^2 is -12i.