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

Answer
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.  

Algebra

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Frederick Koh

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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.

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

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Former straight As A level student from HCJC (aka HCI); scored distinctions in both C and Further Mathematics B Eng (Hons) From The National University Of Singapore (NUS) B Sc (Hons) From University of London External (Grad Route)

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