Math Problem Statement

What is the square root of -16?

Solution

The expression you've provided is the square root of -16, which involves a negative number under the square root. In real numbers, the square root of a negative number is undefined, but in the system of complex numbers, it is represented using the imaginary unit ii, where i2=1i^2 = -1.

To solve 16\sqrt{-16}:

  1. First, we express it as: 16=1×16\sqrt{-16} = \sqrt{-1 \times 16}
  2. Then, break it down: 16=1×16\sqrt{-16} = \sqrt{-1} \times \sqrt{16}
  3. Using 1=i\sqrt{-1} = i and 16=4\sqrt{16} = 4: 16=4i\sqrt{-16} = 4i

Thus, the result is: 16=4i\sqrt{-16} = 4i

Would you like more details or further explanation?

Here are 5 related questions to deepen your understanding:

  1. What is the definition of the imaginary unit ii?
  2. How do we compute square roots of other negative numbers?
  3. What are complex numbers, and how are they represented?
  4. Can we add and multiply complex numbers?
  5. How does the complex plane help visualize complex numbers?

Tip: Imaginary numbers appear when dealing with square roots of negative numbers, and they form the foundation of complex number theory.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Unit

Formulas

√(-a) = √a * i

Theorems

Properties of Square Roots with Negative Numbers
Imaginary Unit Definition (i² = -1)

Suitable Grade Level

Grades 8-10