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# prove it!!!!!!!!!!!!!!!!(2)

Prove that a purely real number can never became equal to a purely imaginary number (Provided that the number is not 0+0i)

Note by Aman Sharma
2 years, 1 month ago

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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. · 2 years, 1 month ago

Thanks for replying you are awsome in proof problems · 2 years, 1 month ago

Thanks! But I wouldn't say I'm awesome. · 2 years, 1 month ago

No, you realy are awsome, also your set ''proof problem of the day'' is realy cool one · 2 years, 1 month ago

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. · 2 years, 1 month ago

I am editing it thanks for pointing out the mistake · 2 years, 1 month ago

Sorry, all real numbers are complex numbers. If this is from NCERT, exercise and problem number please? · 2 years, 1 month ago