Math Problem Statement
Which of these expressions is equivalent to 𝟐+√−𝟑𝟔 ?
Solution
The expression given is . To find an equivalent expression, let's first simplify .
Step-by-step Solution:
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Simplify the square root of a negative number:
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Recognize that is defined as (the imaginary unit):
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Simplify :
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Combine the terms:
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Substitute back into the original expression:
So, the equivalent expression to is .
Would you like a more detailed explanation or have any questions? Here are some related questions that you might find useful:
- What is the imaginary unit and how is it used in complex numbers?
- How do you add and subtract complex numbers?
- What is the significance of the square root of negative numbers in mathematics?
- How can you graph complex numbers on a complex plane?
- What is the difference between real numbers and complex numbers?
Tip: When dealing with square roots of negative numbers, always remember that .
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Imaginary Unit
Square Roots of Negative Numbers
Formulas
√(a * b) = √a * √b
√(-1) = i
Theorems
Properties of Square Roots
Definition of Imaginary Unit
Suitable Grade Level
Grades 9-12