(4i)(-9i).jpeg "(8i)(4i)(-9i)")
Simplifying Complex Number Multiplication
This article will explore the simplification of the complex number multiplication problem: (8i)(4i)(-9i).
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.
Multiplication of Complex Numbers
When multiplying complex numbers, we distribute like any other binomial multiplication. However, we must remember that i² = -1.
Solving the Problem
Let's break down the problem step-by-step:
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Multiply the first two terms: (8i)(4i) = 32i²
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Substitute i² with -1: 32i² = 32(-1) = -32
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Multiply the result by the third term: -32(-9i) = 288i
Therefore, (8i)(4i)(-9i) = 288i.
Conclusion
This example demonstrates the process of multiplying complex numbers. The key is to remember the value of i² and perform the multiplication as you would with any other binomial expression. The final result is a purely imaginary number.