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Multiplying Complex Numbers: (3-4i)(2+i)
This article will demonstrate how to multiply two complex numbers: (3-4i)(2+i).
Understanding Complex Numbers
A complex number is a number 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).
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property, just like we do with real numbers.
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Expand the product: (3 - 4i)(2 + i) = 3(2 + i) - 4i(2 + i)
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Distribute: = 6 + 3i - 8i - 4i²
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Simplify by substituting i² = -1: = 6 + 3i - 8i + 4
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Combine real and imaginary terms: = (6 + 4) + (3 - 8)i
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Final result: = 10 - 5i
Conclusion
Therefore, the product of (3-4i) and (2+i) is 10 - 5i.
Remember, multiplying complex numbers involves applying the distributive property, simplifying using i² = -1, and then combining real and imaginary terms.