Math Problem Statement
Simplify by using the imaginary unit i: (-10 ± √-72) / 2
Solution
To simplify the expression using the imaginary unit :
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Start by addressing the square root of the negative value, . Rewrite it as: Since simplifies further, we have: Therefore:
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Substitute this into the expression:
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Split the numerator for simplification:
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Simplify each term:
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Combine these terms:
Final Answer:
The simplified form is:
Would you like additional details or explanations?
Here are five related questions to deepen understanding:
- How is the imaginary unit defined, and how is it used in calculations?
- What are the properties of square roots involving negative numbers?
- How can you simplify radicals such as step by step?
- What are the typical forms of complex numbers, and how do they appear in equations like this?
- How does the ± symbol affect the solution set of quadratic-like expressions?
Tip: Always simplify radicals as much as possible before proceeding with operations involving imaginary numbers!
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Math Problem Analysis
Mathematical Concepts
Imaginary Numbers
Complex Numbers
Radicals
Algebraic Simplification
Formulas
√(-a) = √a * i
Complex form a + bi
Theorems
Properties of Imaginary Numbers
Radical Simplification
Suitable Grade Level
Grades 9-10