Math Problem Statement

Write the imaginary number in simplified form: the square root of negative 144

Solution

To simplify the square root of a negative number, we use the imaginary unit ii, which is defined as:

i=1i = \sqrt{-1}

Given the square root of 144-144, we can rewrite it as:

144=144(1)=1441\sqrt{-144} = \sqrt{144 \cdot (-1)} = \sqrt{144} \cdot \sqrt{-1}

Since 1=i\sqrt{-1} = i, the expression simplifies to:

144i=12i\sqrt{144} \cdot i = 12i

So, the square root of 144-144 in simplified form is:

12i\boxed{12i}

Would you like further details or have any questions?

Related Questions:

  1. What is the square root of 225-225 in simplified form?
  2. How do you multiply two imaginary numbers?
  3. How do you find the magnitude of a complex number?
  4. What is the cube root of a negative number?
  5. How do you add and subtract imaginary numbers?

Tip: Remember that imaginary numbers are based on the fundamental property that i2=1i^2 = -1.

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Square Roots

Formulas

i = √(-1)
√(-a) = √(a) * i

Theorems

Fundamental Property of Imaginary Numbers: i^2 = -1

Suitable Grade Level

Grades 9-11