Math Problem Statement

√(-49)x

Solution

The expression you provided, 49×x\sqrt{-49} \times x, contains the square root of a negative number. In mathematics, the square root of a negative number involves complex numbers.

49=49×1=7i\sqrt{-49} = \sqrt{49} \times \sqrt{-1} = 7i

Here, ii is the imaginary unit, which satisfies i2=1i^2 = -1. So, the expression becomes:

49×x=7i×x=7ix\sqrt{-49} \times x = 7i \times x = 7ix

Thus, the simplified form of the expression is 7ix7ix, where ii represents the imaginary unit.

Would you like more details on imaginary numbers or complex expressions?

Here are some related questions for further practice:

  1. What is 36×3x\sqrt{-36} \times 3x?
  2. How would you simplify (5i)2(5i)^2?
  3. What is the product of (3+2i)×(1i)(3 + 2i) \times (1 - i)?
  4. What is the magnitude of the complex number 7i7i?
  5. How do you solve the quadratic equation x2+49=0x^2 + 49 = 0?

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

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Numbers
Algebra

Formulas

√(a) × √(b) = √(ab)
√(-1) = i

Theorems

Imaginary Unit Theorem (i^2 = -1)

Suitable Grade Level

Grades 9-12