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Can we order Complex Numbers ? I searched a bit most places says it can but not like the real numbers. I am confused a bit.And I am not sure abouth the truth of those sources.
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The complex numbers don't allow an Archimedean order. This is equivalent to the condition that squares are positive, which is not the case for complex numbers, as ##i^2=-1<0##. They allow however an order like the lexicographical order: ##x+iy < u+iv \Longleftrightarrow x < u \,\vee \, (x=u \wedge y < v)##.Arman777 said:Can we order Complex Numbers ? I searched a bit most places says it can but not like the real numbers. I am confused a bit.And I am not sure abouth the truth of those sources.
Thanks
Complex numbers are numbers that consist of a real part and an imaginary part, usually written in the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e. the square root of -1).
Complex numbers are useful in representing quantities that involve both real and imaginary components. They are commonly used in fields such as engineering, physics, and mathematics to solve problems that cannot be solved with real numbers alone.
Yes, we can order complex numbers. They can be compared using the same rules as real numbers, where the real part is compared first, and if they are equal, then the imaginary part is compared.
To add or subtract complex numbers, we simply add or subtract the real and imaginary parts separately. To multiply complex numbers, we use the FOIL method (First, Outer, Inner, Last) and simplify using the fact that i squared equals -1. To divide complex numbers, we use the conjugate method.
Yes, we can graph complex numbers on a coordinate plane called the complex plane. The horizontal axis represents the real part, while the vertical axis represents the imaginary part. This allows us to visualize and better understand the properties of complex numbers.