Math Problem Statement

Which of these expressions is equivalent to 𝟐+√−𝟑𝟔 ?

Solution

The expression given is 2+362 + \sqrt{-36}. To find an equivalent expression, let's first simplify 36\sqrt{-36}.

Step-by-step Solution:

  1. Simplify the square root of a negative number:

    36=136=136\sqrt{-36} = \sqrt{-1 \cdot 36} = \sqrt{-1} \cdot \sqrt{36}

  2. Recognize that 1\sqrt{-1} is defined as ii (the imaginary unit):

    1=i\sqrt{-1} = i

  3. Simplify 36\sqrt{36}:

    36=6\sqrt{36} = 6

  4. Combine the terms:

    36=6i\sqrt{-36} = 6i

  5. Substitute back into the original expression:

    2+36=2+6i2 + \sqrt{-36} = 2 + 6i

So, the equivalent expression to 2+362 + \sqrt{-36} is 2+6i2 + 6i.

Would you like a more detailed explanation or have any questions? Here are some related questions that you might find useful:

  1. What is the imaginary unit ii and how is it used in complex numbers?
  2. How do you add and subtract complex numbers?
  3. What is the significance of the square root of negative numbers in mathematics?
  4. How can you graph complex numbers on a complex plane?
  5. What is the difference between real numbers and complex numbers?

Tip: When dealing with square roots of negative numbers, always remember that 1=i\sqrt{-1} = i.

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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

Properties of Square Roots
Definition of Imaginary Unit

Suitable Grade Level

Grades 9-12