Math Problem Statement
Use the imaginary number π to rewrite the expression below as a complex number. Simplify all radicals. β β 25
Solution
To rewrite the expression as a complex number, we can use the imaginary unit , where .
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Start with the expression:
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Rewrite using the imaginary unit :
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Now, include the negative sign from the original expression:
Thus, the expression rewritten as a complex number is:
Would you like more details or have any questions about this? Here are some related questions to explore further:
- What is the value of in terms of ?
- How would you express as a complex number?
- If , what is the magnitude of ?
- How do you multiply two complex numbers, say and ?
- What is the complex conjugate of ?
Tip: Remember that . This is fundamental when simplifying expressions involving imaginary numbers.
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Math Problem Analysis
Mathematical Concepts
Imaginary Numbers
Complex Numbers
Radicals
Formulas
i = β(-1)
β(a * b) = βa * βb
Theorems
Properties of Square Roots with Negative Numbers
Suitable Grade Level
Grades 9-11