Math Problem Statement
Express
√
−
5
as a complex number, in terms of i: 5
√ − 5
Solution
To express as a complex number, we can rewrite it in terms of , the imaginary unit, where .
-
Start with the expression:
-
Rewrite as :
-
Use the property :
-
Substitute :
So, the answer is:
Would you like a more detailed explanation, or do you have any questions?
Here are five related questions to deepen understanding:
- How would you express as a complex number?
- What is the general form for the square root of any negative number in terms of ?
- Can you simplify expressions involving higher powers of ?
- What are some practical applications of imaginary numbers in physics or engineering?
- How do complex numbers help in solving quadratic equations with no real solutions?
Tip: When simplifying square roots of negative numbers, remember that allows you to express any negative square root in terms of positive values.
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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
Definition of the Imaginary Unit (i)
Suitable Grade Level
Grades 10-12