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Multiplying Complex Numbers: (7i-3)(2+6i)
This article will guide you through the process of multiplying two complex numbers: (7i-3)(2+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 Process
We can multiply complex numbers using the distributive property, similar to multiplying binomials:
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Distribute the first term of the first complex number: (7i - 3) * 2 = 14i - 6
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Distribute the second term of the first complex number: (7i - 3) * 6i = 42i² - 18i
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Combine the results: 14i - 6 + 42i² - 18i
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Simplify using the fact that i² = -1: 14i - 6 - 42 - 18i
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Combine like terms: -48 - 4i
The Result
Therefore, the product of (7i-3)(2+6i) is -48 - 4i.
Conclusion
Multiplying complex numbers involves applying the distributive property and simplifying using the fact that i² = -1. This process leads to a new complex number, in this case, -48 - 4i.