What is the modulus of 3+4i?

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'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?

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Find the four roots of the equation z^4 = + 8(sqrt(3) + i), in the form z = r*e^(i*theta). Draw the roots on an argand diagram.

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What is De Moivre's theorem?

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The ODE mx'' + cx' + kx = 0 is used to model a damped mass-spring system, where m is the mass, c is the damping constant and k is the spring constant. Describe and explain the behaviour of the system for the cases: (a) c^2>4mk; (b) c^2=4mk; (c) c^2<4mk.

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