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Prove that 2 complex numbers a+ib and c +id are equal if a =c and b=d.

Two complex numbers are equal if the real and imaginary parts of both the complex numbers are equal.

Consider two real numbers, a + ib and c + id.

They are equal if real parts a = c and imaginary parts b = d.

But this is not valid in the case of real numbers.

As, 2 + 3 = 4 + 1  does not mean, 2 = 3 and 4 = 1.

The answer posted by DebojeetM is correct.

@DebojeetM: Good answer. Keep  posting!!

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 Given 

a+ib = c +id................(1)

On equating the real and imaginary parts of the equation (1)

we have, a=c and b=d..

Hence proved.

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Nope, I mean 2+3=4+1 does not necessarily mean 2=4 or 3=1! Please explain.

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 No others conditions given??

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 the logic put forward by you by u is absolutely correct..

But keep in mind the real and imaginary part.. the example given by you is not in the context of complex numbers. your example is based on whole numbers

The complex number expresssed in A+iB form has a real part(ie A) and imaginary part(ie B). So i equated both and proved a=c and b=d.

please let me know your feedback...

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Hm... maybe... but why can't a similar condition(like the condition presented by me) be there in the case of complex numbers? I mean ok there's a real part and an imaginary part but are they always separate?

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