(-3-4i)(-1-6i).jpeg "(-2i)(-3-4i)(-1-6i)")
Multiplying Complex Numbers: A Step-by-Step Guide
This article will walk you through the process of multiplying the complex numbers (-2i)(-3-4i)(-1-6i).
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
To multiply complex numbers, we treat i like a variable and use the distributive property (also known as FOIL for binomials) to multiply the terms. Remember that i² = -1.
Solving the Problem
Let's multiply the complex numbers step by step:
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Multiply the first two factors: (-2i)(-3-4i) = 6i + 8i² Since i² = -1, we can substitute: 6i + 8i² = 6i + 8(-1) = -8 + 6i
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Multiply the result from step 1 by the third factor: (-8 + 6i)(-1 - 6i) = 8 + 48i - 6i - 36i² Substituting i² = -1: 8 + 48i - 6i - 36i² = 8 + 48i - 6i + 36 = 44 + 42i
Final Answer
Therefore, the product of the complex numbers (-2i)(-3-4i)(-1-6i) is 44 + 42i.