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Let P(n) be the statement that 11ⁿ - 6 is divisible by 5.

BASE CASE: Let n = 1.  This gives 11¹ - 6 = 5, ...

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 ...