how to represent (set of all complex numbers)^2? I know that set of all complex numbers is just a+bi

Question

anonymous · Answer

thanks @Hoa

anonymous · Answer

a^2 +2abi -b^2
Is this what you're asking?

turingtest · Answer

the set of all complex numbers is usually represented by $\mathbb C$...

anonymous · Answer

somewhat, it is just a general form of (all set of complex number)^2$$C^2$$

turingtest · Answer

$\mathbb C^2$ would be a 2-dimensional complex vector space

anonymous · Answer

Obtained by squaring (a+bi)
(a+bi)(a+bi)
= a^2 + abi +abi +b^2i^2
=a^2 +2abi +b^2*(-1)
= a^2 + 2abi -b^2

anonymous · Answer

Yeah, what Turing said is the only other way to interpret this, from what I can tell.
It would be the set of CxC basically, which means ordered pairs of complex numbers.
The set would consist of
(a+bi, c+di)

sirm3d · Answer

$$\large {a+bi\in \mathbb C\(a+b)^2=(a^2-b^2)+(2ab)i\in \mathbb C}$$

anonymous · Answer

so who's right?

sirm3d · Answer

try posting the original question.

anonymous · Answer

What is the dimension of $$C^2$$as a real vector? @sirm3d

sirm3d · Answer

now, it's clear. @TuringTest is right.

anonymous · Answer

Unless you understand the question very well, paraphrasing what is asked is usually a bad idea. Very often, you'll word things in an unclear manner or leave out critical information.

anonymous · Answer

which is my weakness @SmoothMath