Math Problem Statement

Express squareroot-4 as a complex number: squareroot-4=

Solution

The square root of 4-4 is expressed as a complex number using the imaginary unit ii, where i=1i = \sqrt{-1}.

4=41=2i\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i

So:

4=2i\sqrt{-4} = 2i

Would you like further clarification on this concept?


Related Questions:

  1. What is the square root of 9-9 expressed as a complex number?
  2. How do we define the imaginary unit ii in mathematics?
  3. Can you calculate higher powers of ii, such as i3i^3 or i4i^4?
  4. What is the general form of a complex number?
  5. How can complex numbers be visualized on a coordinate plane?

Tip: Remember that when dealing with negative square roots, always represent them using the imaginary unit ii.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Square Roots
Imaginary Numbers

Formulas

\sqrt{-a} = \sqrt{a} \cdot i

Theorems

Definition of imaginary unit i

Suitable Grade Level

Grades 9-12