Problem 83 - Introductory Algebra for College Students

Question

In your own words, state the Pythagorean Theorem.

Step-by-Step Solution

Answer

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The formula is: \( c^2 = a^2 + b^2 \).

Step 1: Identify the Complex Number Operation

We need to perform the operation: \(In your own words, state the Pythagorean Theorem.\).

Step 2: Apply Complex Number Rules

We separate the real and imaginary parts. Remember that \(i = \sqrt{-1}\) and \(i^2 = -1\).

Step 3: Combine Like Terms

We combine the real parts together and the imaginary parts together.

Step 4: State the Result

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The formula is: \( c^2 = a^2 + b^2 \).