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Multiplying Complex Numbers: (7-3i)(8+4i)
This article will guide you through multiplying the complex numbers (7-3i) and (8+4i).
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 (i.e., i² = -1).
Multiplication Process
To multiply complex numbers, we use the distributive property (also known as FOIL - First, Outer, Inner, Last):
- Multiply the First terms: 7 * 8 = 56
- Multiply the Outer terms: 7 * 4i = 28i
- Multiply the Inner terms: -3i * 8 = -24i
- Multiply the Last terms: -3i * 4i = -12i²
Simplifying the Result
Now, we have: 56 + 28i - 24i - 12i²
Since i² = -1, we can substitute: 56 + 28i - 24i - 12(-1)
Combining the real and imaginary terms: 56 + 12 + 28i - 24i = 68 + 4i
Final Answer
Therefore, the product of (7-3i) and (8+4i) is 68 + 4i.