Math Problem Statement
Use square roots to solve the equation x^2 = -64 over the complex numbers. Select any solutions that apply.
Solution
Let's solve the given equation step by step:
The equation is:
Step 1: Solve for using square roots
To find , take the square root of both sides:
Step 2: Simplify
Using the property of square roots with negative numbers, , where is the imaginary unit, we can rewrite:
Thus, the solutions are:
Final Answer:
The correct solutions are:
Options that match:
- A.
- D.
Would you like further clarification or detailed steps on this?
Here are 5 related questions to expand your understanding:
- How does the imaginary unit relate to negative square roots?
- Can you explain the difference between real and complex numbers?
- What are some practical applications of complex numbers in physics or engineering?
- How do you represent complex solutions on the complex plane?
- Why does not have real square roots?
Tip: Always remember that square roots of negative numbers lead to complex solutions involving .
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Square Roots
Imaginary Unit
Formulas
\( \sqrt{-a} = i\sqrt{a} \)
Theorems
Properties of Imaginary Numbers
Suitable Grade Level
Grades 9-12