If the number 𝑍 equals eight plus 𝑖 is represented on an Argand diagram by the point 𝐴, determine the Cartesian coordinates of that point.
To answer this question, we absolutely could go ahead and plot the complex number 𝑍 on the Argand diagram and then read the information from there. But that’s quite a long-winded way to go about answering this question. Instead, we remind ourselves of the definition of the Argand diagram. We know that a complex number of the form 𝑥 plus 𝑦𝑖 can be represented by a point whose Cartesian coordinates are 𝑥, 𝑦. The real part is the 𝑥-coordinate. And the imaginary part is the 𝑦-coordinate.
The real part of our complex number is eight. And we can figure the imaginary part as the coefficient of 𝑖. So in this case, the imaginary part of 𝑍 is one. This means the Cartesian coordinates of the point that represents the complex number 𝑍 on the Argand plane are eight, one.