%5E2(6i).jpeg "(7i)^2(6i)")
Simplifying Complex Numbers: (7i)²(6i)
This article will walk you through the process of simplifying the expression (7i)²(6i), which involves operations with complex numbers.
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).
Simplifying the Expression
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Expand the square: (7i)² = (7i)(7i) = 49i²
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Substitute i² with -1: 49i² = 49(-1) = -49
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Multiply by 6i: -49 * 6i = -294i
Therefore, the simplified form of (7i)²(6i) is -294i.
Key Points
- Imaginary unit: Remember that i² = -1.
- Order of operations: Follow the order of operations (PEMDAS/BODMAS) when simplifying complex expressions.
- Real and imaginary parts: The final result is a purely imaginary number, as it only has an imaginary component.