A pure imaginary number is of the form \(bi\) where \(b\) is a [non-zero] real number and \(i^2=-1\).

If \(a\) real number were equal to \(bi\), then we would have \(a^2=-b^2\) which is impossible since the right hand side is negative while the left hand side is non-negative.

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TopNewestA pure imaginary number is of the form \(bi\) where \(b\) is a [non-zero] real number and \(i^2=-1\).

If \(a\) real number were equal to \(bi\), then we would have \(a^2=-b^2\) which is impossible since the right hand side is negative while the left hand side is non-negative.

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Thanks for replying you are awsome in proof problems

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Thanks! But I wouldn't say I'm awesome.

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Actually, by the definition of complex numbers, a real number is also considered a complex number. Think of it as like, we can write x as x + 0i.

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I am editing it thanks for pointing out the mistake

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Sorry, all real numbers are complex numbers. If this is from NCERT, exercise and problem number please?

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Edited

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