Write sin(4x) in terms of sin and cos.

4sinx(cosx)^3 - 4cosx(sinx)^3

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Find the modulus and argument of the complex number 1+2i


A tank contains 500L of salty water. Pure water is pumped in at a rate of 10 L/sec, and the the mixture is pumped out at a rate of 15L/ sec. If the concentration of salt is 5g/L initially, form an equation of amount of salt, s, at t seconds.


Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.


Prove De Moivre's by induction for the positive integers


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