Math Problem Statement

Multiply: (√(-9)) * (√(-49))

Solution

Let's analyze the expression:

(9)(49)(\sqrt{-9}) \cdot (\sqrt{-49})

  1. The square roots of negative numbers involve imaginary numbers. Specifically: 9=3i(since 9=3 and 1=i)\sqrt{-9} = 3i \quad \text{(since } \sqrt{9} = 3 \text{ and } \sqrt{-1} = i\text{)} 49=7i(since 49=7 and 1=i)\sqrt{-49} = 7i \quad \text{(since } \sqrt{49} = 7 \text{ and } \sqrt{-1} = i\text{)}

  2. Now multiply these two expressions: (3i)(7i)=21i2(3i) \cdot (7i) = 21i^2

  3. Since i2=1i^2 = -1, we get: 21i2=21×(1)=2121i^2 = 21 \times (-1) = -21

Thus, the simplified answer is:

21-21

Would you like more details on any step?

Here are 5 related questions for practice:

  1. What is 16\sqrt{-16}?
  2. How do you simplify i4i^4?
  3. Multiply 4\sqrt{-4} and 16\sqrt{-16}.
  4. Simplify (5i)×(6i)(5i) \times (6i).
  5. What is the result of i3i^3?

Tip: Always remember that i2=1i^2 = -1, which is crucial in simplifying expressions with imaginary numbers!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Numbers

Formulas

√(a) * √(b) = √(a*b)
i^2 = -1

Theorems

Properties of Imaginary Numbers

Suitable Grade Level

High School