Math Problem Statement

Simplify the imaginary number. 18

−1

−16

Solution

It seems like you want to simplify a complex expression, but it's a bit unclear how the terms are related. Based on what you've written, I assume you're referring to the square roots of negative numbers, possibly:

18116\sqrt{-18} - \sqrt{-1} - \sqrt{-16}

In this case, we can simplify each square root of the negative numbers by using the imaginary unit ii, where i=1i = \sqrt{-1}.

Let's break it down:

  1. 18=18i=32i\sqrt{-18} = \sqrt{18} \cdot i = 3\sqrt{2} \cdot i
  2. 1=i\sqrt{-1} = i
  3. 16=16i=4i\sqrt{-16} = \sqrt{16} \cdot i = 4 \cdot i

Now we can rewrite the expression:

32ii4i3\sqrt{2}i - i - 4i

Combine the imaginary terms:

32i(1+4)i=32i5i3\sqrt{2}i - (1 + 4)i = 3\sqrt{2}i - 5i

Thus, the simplified expression is:

32i5i3\sqrt{2}i - 5i

This is the simplified form of the original expression.


Would you like more details on simplifying complex numbers or operations with imaginary numbers?

Here are 5 related questions:

  1. What are the basic rules for working with imaginary numbers?
  2. How do you add or subtract complex numbers?
  3. How can you simplify higher-order square roots of negative numbers?
  4. What is the geometric representation of complex numbers on the complex plane?
  5. How do you multiply or divide complex numbers?

Tip: When simplifying complex expressions, always try to factor out the imaginary unit ii to make the calculations easier!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Numbers
Square Roots

Formulas

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

Theorems

Imaginary unit (i) where i = \sqrt{-1}

Suitable Grade Level

Grades 9-11