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Find the modulus and argument of the complex number 1+2i

It is always helpful to start by drawing a diagram with a Real and Imaginary axis then plotting the number (in our case 1+2i) on the diagram and drawing a line from the origin to our point. Remember the m...

Answered by Thomas C. • Further Mathematics tutor

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How do I construct a proof by induction?

There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof.

The base case consists of proving that a statement is true for ...

Answered by Alex F. • Further Mathematics tutor

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Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)

tanh(x) = ((e^x-e^-x)/2)/((e^x+e^-x)/2) 1 - tanh²(x) = 1-((e^x-e^-x)/(e^x+e^-x))² = ((e^2x+...

Answered by Chris B. • Further Mathematics tutor

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x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x³+ 2x²- 9x - 18. However it is very difficult to approach the problem like thi...

Answered by Chris B. • Further Mathematics tutor

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Factorise 6x^2 + 7x + 2

6x^2 + 7x + 2 can be written in the form ax^2 + bx + c. In order to factorise this I use the following method which can be used to factorise similar equations. Multiply 'a' and 'c' to get ac (here this is...

Answered by Hannah P. • Further Mathematics tutor

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