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Find a quadratic equation with integral coefficients having the given roots i√ 5 , -i√ 5

The two factors associated with this equation are

z- i√ 5  and  z -(- i√ 5) = z + i√ 5 .

Hence, the required equation is simply given by

(z- i√ 5)(z + i√ 5) = 0

z^2 - (i√ 5)^2 = 0         (Note the expansion (a-b)(a+b)=a^2-b^2 is used here)

Since i^2 = -1          (i is the imaginary number = √ -1 )

the above reduces to

z^2 + 5 = 0  (shown)

Hope this helps. Peace.  


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Frederick Koh


I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.


More than 7 years of experience helping out in various homework forums. Latest presence is over at You can also visit my main maths website where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

IEEE(Institute of Electrical and Electronics Engineers )

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