Problem 106 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A complex number \(a+b i\) can be interpreted geometrically as the point \((a, b)\) in the \(x y\) -plane.

Step-by-Step Solution

Answer

The statement makes sense. Each complex number \(a + bi\) can be interpreted geometrically as a point in the \(xy\)-plane where 'a' is the x-coordinate and 'b' is the y-coordinate.

Step 1: Understand Complex Numbers

A complex number can be written in the form \(a + bi\), where \(a\) and \(b\) are real numbers and \(i\) is the imaginary unit, which has the property \(i^2 = -1\). 'a' is referred to as the real part and 'b' as the imaginary part of the complex number.

Step 2: Geometrical interpretation

A complex number \(a + bi\), represented in the form (a, b), is associated with a point in the Euclidean plane. Here, 'a' is positioned on the x-axis representing the real parts and 'b' on y-axis representing the imaginary parts.