(-4%2B3i).jpeg "(2-6i)(-4+3i)")
Multiplying Complex Numbers: (2-6i)(-4+3i)
This article will explore the multiplication of two complex numbers: (2-6i) and (-4+3i).
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).
Multiplication Process
To multiply complex numbers, we use the distributive property, similar to how we multiply binomials.
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Expand the product: (2-6i)(-4+3i) = 2(-4) + 2(3i) - 6i(-4) - 6i(3i)
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Simplify by multiplying: = -8 + 6i + 24i - 18i²
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Substitute i² with -1: = -8 + 6i + 24i - 18(-1)
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Combine real and imaginary terms: = -8 + 18 + 6i + 24i
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Final result: = 10 + 30i
Conclusion
Therefore, the product of (2-6i) and (-4+3i) is 10 + 30i. This demonstrates the process of multiplying complex numbers using the distributive property and substituting i² with -1.