Cartesian <-> a+bi conversion

Question

For the question in the image,

Question and my answer

I answered this question with (1/root5, -1/root5), which correspond to x and y value in Cartesian coordinate.

However, the correct answer for this question says, 1/5-3i/5, as following picture:

Correct answer for this question

What I actually did is to convert that 1/5-3i/5 into x and y form using x=rcos(theta) and y=rsin(theta), becuz I thought x and y value represents Cartesian coordinate if it is about 2 dimensional.

So my question is, does that form of a+bi really represents Cartesian coordinate?

Answer 1

$a+bi\ $ represents coordinates in the complex plane, where $a$ is the real component, and $b$ is the complex component.

The Cartesian plane can be used to represent any complex number. Your answer was to be given in Cartesian coordinates.

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