Math Problem Statement
√-36
Solution
The expression shown in the image is .
Since the square root of a negative number is not defined in the set of real numbers, we must consider complex numbers. In the realm of complex numbers, the square root of a negative number involves the imaginary unit , where .
Thus:
So, the answer is , where is the imaginary unit.
Would you like further details on this, or do you have any questions?
Here are five related questions to further explore this topic:
- What is the square root of other negative numbers like ?
- Can the square root of any negative number be simplified similarly?
- What is the definition of the imaginary unit ?
- How do we perform operations (addition, multiplication, etc.) with imaginary numbers?
- Can real and imaginary numbers be combined in other ways to form complex numbers?
Tip: The square of the imaginary unit is , which is fundamental in calculations involving complex numbers.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Square Roots
Imaginary Unit
Formulas
√-a = i√a, where i = √-1
Theorems
Imaginary Unit Theorem: i^2 = -1
Suitable Grade Level
Grades 9-12