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Further Mathematics

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The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form rexp(iTheta), where r>0 and -pi < theta <= pi. By using the form rexp(iTheta) solve the equation z^5 = -2sqrt(2) + 2sqrt(6)i.

Using an argand diagram we can see that this (in fact all) complex numbers create a right angled triangle and using this fact we can find the modulus of this number. The modulus of this number is the 'r' ...

Answered by Tajmeet G. • Further Mathematics tutor

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Show that G = {1, -1} is a group under multiplication.

We must prove the four axioms of a group are satisfied (i.e Identity, Associativity, Closure, and Invertibility). Identity: The identity element is an element e in G such that e

Answered by Ross T. • Further Mathematics tutor

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Cube roots of 8?

8 traditionally has 1 cube root. 2. This is only the real root. It has 2 more complex roots!How can we see this?Consider a vector on the argand diagram. If we square it. What happens to it's magnitude and...

Answered by Vishal J. • Further Mathematics tutor

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Differentiate: y=x^x

First take log’s each side as it would turn our complicated function into something differentiable by chain rule.
ln y = x*ln x
Then differentiate y with respect to x:
d(ln y)/dx = ln x + 1...

Answered by Mihai V. • Further Mathematics tutor

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Use induction to prove that for all positive integers n, f(n)=2^(3n+1)+3x5^(2n+1) is divisible by 17.

Prove the basis to be true. Let n=1 and this gives f(1)=16+375=391 which is divisible by 17. Now assume that if we let n=k f(k) is divisible by 17. If we now let n=k+1 and prove f(k+1) is divisible by 17 ...

Answered by Marijn H. • Further Mathematics tutor

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