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The complex conjugate of a complex number is a number for which the real part is the same and for which the imaginary part has the same magnitude but opposite sign. e.g. the complex conjugate of 6+7i is 6...

Integrating the acceleration function gives the velocity function v, as below:
v = t² +5t +C₁, where C₁ is a constant.

Integrating the velocity func...

There are two obvious approaches here:
1. Solve the equation x² - 2x + 2 = 0 to find A and B and then calculate the required values.

2. Or we can use the quicker method of ana...

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 ...

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 follo...