-(1-i)(2%2B3i)(4-4i).jpeg "(b) (1-i)(2+3i)(4-4i)")
Simplifying Complex Number Multiplication
This article explores the simplification of the complex number expression (1 - i)(2 + 3i)(4 - 4i).
Understanding Complex Numbers
Complex numbers are numbers of the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).
Step-by-Step Simplification
To simplify the given expression, we'll multiply the complex numbers step-by-step:
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Multiply the first two factors: (1 - i)(2 + 3i) = (1 * 2) + (1 * 3i) + (-i * 2) + (-i * 3i) = 2 + 3i - 2i - 3i² = 2 + i + 3 (since i² = -1) = 5 + i
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Multiply the result from step 1 by the third factor: (5 + i)(4 - 4i) = (5 * 4) + (5 * -4i) + (i * 4) + (i * -4i) = 20 - 20i + 4i - 4i² = 20 - 16i + 4 (since i² = -1) = 24 - 16i
Conclusion
Therefore, the simplified form of the complex number expression (1 - i)(2 + 3i)(4 - 4i) is 24 - 16i.