(2i)%5E2.jpeg "(3i)(2i)^2")
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
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Simplify the exponent: (2i)^2 = (2i)(2i) = 4i^2
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Substitute i^2 with -1: 4i^2 = 4(-1) = -4
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Multiply with the remaining term: (3i)(-4) = -12i
Final Answer
Therefore, the simplified form of (3i)(2i)^2 is -12i.