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Multiplying Complex Numbers: (9 - 4i)(2 + 9i)
This article will guide you through the process of multiplying two complex numbers, specifically (9 - 4i)(2 + 9i).
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 multiplying binomials in algebra:
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Expand the product: (9 - 4i)(2 + 9i) = 9(2 + 9i) - 4i(2 + 9i)
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Distribute: = 18 + 81i - 8i - 36i²
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Simplify using i² = -1: = 18 + 81i - 8i + 36
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Combine real and imaginary terms: = (18 + 36) + (81 - 8)i
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Final result: = 54 + 73i
Conclusion
Therefore, the product of (9 - 4i)(2 + 9i) is 54 + 73i. This process demonstrates how to multiply complex numbers and arrive at a simplified complex number expression.