What is a complex number?

A complex number is a number that consists of two parts, a real part, like any number you have been dealing with since you started learning maths, and an imaginary number, often tagged along with a i or a j, for example a+bi. The best way to imagine it is as a vector on a plane, the point not unlike one on a x,y axes but instead on a real, imaginary axes. 

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Related Further Mathematics A Level answers

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It is given that f(x) = 2sinhx+3coshx. Show that the curve y = f(x) has a stationary point at x =-½ ln(5) and find the value of y at this point. Solve the equation f(x) = 5, giving your answers exactly


(FP1) Given k = q + 3i and z = w^2 - 8w* - 18q^2 i, and if w is purely imaginary, show that there is only one possible non-zero value of z


Given that α= 1+3i is a root of the equation z^3 - pz^2 + 18z - q = 0 where p and q are real, find the other roots, then p and q.


Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)