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Does it have something to do with the quadratic form? What would i type on google to search for more information to get better search results?
To summarize what MisterX and Jamma said, we often write complex numbers like that because it is convenient (it fits our commonly used xy- coordinate system format) but there are many different ways in which we could write complex numbers: [itex]re^{i\theta}[/itex] is one. Engineers often use the format "[itex]r cis(\theta)[/itex]" which is short for "[itex]r(cos(\theta)+ i sin(\theta))= re^{i\theta}[/itex]" as Jamma said.Does it have something to do with the quadratic form? What would i type on google to search for more information to get better search results?
You might find this article helpful:But what about the "+" sign in between the real part and the imaginary part? Since graphing complex numbers on the complex plane is alot like graphing real numbers on the real plane, why didn't we use a comma inbetween the real parts and complex parts?
How do we know there are nice properties such as addition and multiplication for something in the form "A+Bi"? If we had instead used the convention "(A,Bi)" to graph complex numbers, then would it still have had addition and multiplication for complex numbers? It seems a bit odd to me. You can of course multiply a scalar with (a,bi) or add another complex number but it would've done differently.
with the current system, (a+bi)^2 = a^2 + 2(a)(bi) -b^2. would it still have resulted in the same if we would have multiplied (a,bi) with (a,bi)? How do we even do that?
Does it have something to do with the quadratic form? What would i type on google to search for more information to get better search results?
Here is a thought, maybe helpful.To summarize what MisterX and Jamma said, we often write complex numbers like that because it is convenient (it fits our commonly used xy- coordinate system format) but there are many different ways in which we could write complex numbers: [itex]re^{i\theta}[/itex] is one. Engineers often use the format "[itex]r cis(\theta)[/itex]" which is short for "[itex]r(cos(\theta)+ i sin(\theta))= re^{i\theta}[/itex]" as Jamma said.
There is no "mathematical" reason- it is just a convention.