Math Problem Statement

solve the following equations for x = -4 √(-49)x=

Solution

The equation involves a square root of a negative number, specifically 49\sqrt{-49}. The square root of a negative number is not a real number; instead, it is an imaginary number.

49=7i\sqrt{-49} = 7i

Given this, the equation becomes:

x=7ix = 7i

Since you want the value of xx for x=4x = -4, the equation x=7ix = 7i remains valid as is, and no substitution or further solution for xx is needed. The expression x=7ix = 7i means that xx is an imaginary number.

Would you like more details or have any questions? Here are some related questions you might consider:

  1. What are imaginary numbers, and how are they used in mathematics?
  2. How do we interpret and solve equations involving complex numbers?
  3. What is the difference between real numbers and imaginary numbers?
  4. How do you perform arithmetic operations with complex numbers?
  5. Can you provide examples of real-world applications where imaginary numbers are used?

Tip: Imaginary numbers are represented as ii where i=1i = \sqrt{-1}. They are often used in engineering and physics to solve problems involving waveforms and oscillations.

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Complex Numbers

Formulas

Square Root of a Negative Number: √(-a) = i√a

Theorems

Definition of Imaginary Unit (i)

Suitable Grade Level

Grades 9-12