Math Problem Statement
Multiply (√(-16)) (√(-25)) and simplify your answer.
Solution
The expression you're being asked to simplify is:
Here’s how to approach it:
-
Simplify each square root:
- (where is the imaginary unit, because ).
- .
-
Multiply the simplified results:
-
Simplify further using the fact that :
So, the simplified answer is -20.
Would you like more details, or do you have any questions about this solution?
Here are 5 related questions to deepen understanding:
- What is the general rule for simplifying square roots of negative numbers?
- Why is defined as in complex numbers?
- How would you multiply other complex numbers like and ?
- What happens if you have square roots with mixed real and imaginary components, like ?
- How do you graph complex numbers on the complex plane?
Tip: Always handle imaginary numbers carefully, making sure to simplify when multiplying them!
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Math Problem Analysis
Mathematical Concepts
Imaginary Numbers
Complex Numbers
Multiplication of Square Roots
Formulas
√(-a) = i√(a)
i² = -1
Theorems
Properties of Imaginary and Complex Numbers
Suitable Grade Level
Grades 9-12