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The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2

If the roots of this cubic equation are a, b and c, then the equation can be written(z - a)(z - b)(z - c) = 0multiplying this out gives:z^3 - az^2 - bz^2 - cz^2 + abz + acz + bcz - abcgrouping terms with z t...
EH
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Prove that sum(k) from 0 to n is n(n+1)/2, by induction

Proof by induction involves making an assumption, and using that assumption to prove that the consecutive case follows the pattern. The key to this is realising that most questions follow the same structure,...
NR
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What is a complex number?

A complex number is a number that consists of two parts, a real part, like any number you have been dealing with since you started learning maths, and an imaginary number, often tagged along with a i or a j,...
PB
4689 Views

How does proof by mathematical induction work?

Mathematical induction is a way of proving statements in maths. The principle is quite similar to dominoes (not pizza, the game) - if you push the first one, the second one will be pushed over, pushing the t...
SC
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What modules have you done before?

C1, C2, C3, C4 D1 FP1, FP2, FP3 M1, M2 S1, S2
ZK
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