Math Problem Statement
solve
Use square roots to solve the equation x² = -25 over the complex numbers. Select all solutions for the equation.
Solution
To solve the equation over the complex numbers, we follow these steps:
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Rewrite the equation:
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Take the square root of both sides:
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Recall that can be expressed as . Using , we get:
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Therefore, the solutions are:
The two solutions are:
Correct Answers:
Let me know if you'd like further explanation or have any questions. Here are 5 related questions to expand your understanding:
- What is the general process for solving equations involving complex numbers?
- How do square roots of negative numbers work in terms of imaginary numbers?
- Why is an essential property in complex numbers?
- Can you solve similar equations like or ?
- What is the geometric interpretation of solutions like on the complex plane?
Tip: When solving equations involving complex numbers, always express negative square roots in terms of , and check for both positive and negative solutions!
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Square Roots
Imaginary Numbers
Formulas
x² = -a implies x = ±√(-a)
√(-a) = √a * i where i² = -1
Theorems
Properties of Square Roots
Definition of Imaginary Unit (i² = -1)
Suitable Grade Level
Grades 9-12