(-2i)-5(3%2B5i).jpeg "(-4i)(-2i)-5(3+5i)")
Simplifying Complex Expressions: A Step-by-Step Guide
This article will guide you through simplifying the complex expression (-4i)(-2i) - 5(3 + 5i). We'll break down each step and explain the principles involved.
Understanding Complex Numbers
Before diving into the problem, let's refresh our understanding of complex numbers. A complex number is a number that can be written in the form a + bi, where:
- a and b are real numbers.
- i is the imaginary unit, defined as the square root of -1 (i² = -1).
Simplifying the Expression
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Multiply the first two terms: (-4i)(-2i) = 8i²
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Substitute i² with -1: 8i² = 8(-1) = -8
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Distribute the -5: -5(3 + 5i) = -15 - 25i
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Combine the results: (-8) + (-15 - 25i) = -23 - 25i
Final Answer
The simplified form of the expression (-4i)(-2i) - 5(3 + 5i) is -23 - 25i.
Key Points
- Remember that i² = -1 is a fundamental property of complex numbers.
- Use the distributive property to multiply complex numbers.
- Combine the real and imaginary parts separately to obtain the final result.
By following these steps, you can confidently simplify complex expressions and arrive at the correct answer.