Comparing complex numbers?

I know that for $a_1i+b_1$ and $a_2i+b_2$ where $a_1\ne a_2$, we can only compare the magnitudes of the complex numbers. But what if $a_1=a_2$? For example, is $3i+2\gt3i-1$?

#Algebra

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Comments

In my opinion, any of the following comparisons are valid for complex numbers:

1) Compare the real parts
2) Compare the imaginary parts
3) Compare the polar magnitudes of the complex numbers
4) Compare the polar phase angles of the complex numbers

Steven Chase - 1 year, 10 months ago

So, is my comparison valid?

Ruilin Wang - 1 year, 10 months ago

You could say $|3i + 2| > |3i - 1|$ if you want to compare magnitudes, for example. The problem is that "greater than" is ambiguous when applied to complex numbers. We have to explicitly resolve the ambiguity by saying exactly what aspect of the complex numbers we are comparing.

Steven Chase - 1 year, 10 months ago

@Steven Chase – Okay, thanks!

Ruilin Wang - 1 year, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$