(1-4i)(1%2Bi).jpeg "(2i)(1-4i)(1+i)")
Simplifying Complex Numbers: (2i)(1-4i)(1+i)
This article will guide you through the process of simplifying the complex number expression: (2i)(1-4i)(1+i)
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.
Simplifying the Expression
To simplify the given expression, we'll use the distributive property and the fact that i² = -1.
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Start with the first two factors: (2i)(1-4i) = 2i - 8i²
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Substitute i² with -1: 2i - 8(-1) = 2i + 8
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Now, multiply the result by the third factor: (2i + 8)(1 + i) = 2i + 2i² + 8 + 8i
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Again, substitute i² with -1: 2i - 2 + 8 + 8i = 6 + 10i
Final Result
Therefore, the simplified form of the complex number expression (2i)(1-4i)(1+i) is 6 + 10i.