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FP1 Key Notes
Chapter 1 ­ Complex Numbers

i2 = -1
When adding/subtracting imaginary numbers, just add/subtract real
and imaginary parts

i.e. (4+3i) + (7+8i) = 11+11i
(17+2i) ­ (9+8i) = 8-6i

The complex conjugate of a+bi is a-bi. You multiply an imaginary
number by its complex conjugate pair to…

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Chapter 2 ­ Numerical Solutions of Equations

If you find an interval in which f(x) changes sign, the interval must
contain a root of f(x) = 0
Use the interval bisection method to find an approximation of the root
(trial and improvement to find when the sign changes)
Newton-Raphson formula…

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For a rectangular hyperbola, the equation is given in the form xy = c2
Where general points are given as x = ct2 and y= c/t

Chapter 4 ­ Matrix Algebra

To add or subtract matrices you simply add or subtract the
corresponding elements of the two matrices
Multiply matrices…

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Step 5 ­ Write conclusion: It's true for n=1, if it's true for n=k, then it's true for
n=k+1. Therefore, by mathematical induction, it's true for all n Z+

Tom Fenton


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