(-4-3i)(7%2B8i).jpeg "(-2-2i)(-4-3i)(7+8i)")
Multiplying Complex Numbers
This article will explore the multiplication of three complex numbers: (-2 - 2i)(-4 - 3i)(7 + 8i).
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 distribute just like with binomials. However, we must remember that i² = -1.
Calculating the Product
Let's break down the multiplication step by step:
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Multiply the first two complex numbers: (-2 - 2i)(-4 - 3i) = 8 + 6i + 8i + 6i² = 8 + 14i + 6(-1) = 2 + 14i
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Multiply the result by the third complex number: (2 + 14i)(7 + 8i) = 14 + 16i + 98i + 112i² = 14 + 114i + 112(-1) = -98 + 114i
Result
Therefore, the product of the complex numbers (-2 - 2i)(-4 - 3i)(7 + 8i) is -98 + 114i.
Conclusion
Multiplying complex numbers requires understanding the properties of the imaginary unit i. By using the distributive property and simplifying using the fact that i² = -1, we can effectively multiply complex numbers and arrive at the correct result.