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Multiplying Complex Numbers: (7 + 2i)(9 - 6i)
This article will demonstrate how to multiply two complex numbers: (7 + 2i) and (9 - 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 (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: (7 + 2i)(9 - 6i) = 7(9 - 6i) + 2i(9 - 6i)
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Distribute: = 63 - 42i + 18i - 12i²
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Simplify by substituting i² with -1: = 63 - 42i + 18i + 12
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Combine real and imaginary terms: = (63 + 12) + (-42 + 18)i
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Final Result: = 75 - 24i
Therefore, the product of (7 + 2i) and (9 - 6i) is 75 - 24i.
Conclusion
Multiplying complex numbers involves applying the distributive property and simplifying by substituting i² with -1. This process results in a new complex number, expressed in the standard form a + bi.