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|Z| = sqrt(1/2^2 + (sqrt(3)/2)^2) = 1 arg(Z) = arctan((sqrt(3)/2)/(1/2)) = pi/3 Z = cos(pi/3) + jsin(pi/3) Z = e^j(pi/3) Apologies for the use of sqrt(), I have no way yet of using the symbol on my laptop...

First we must differentiate the equation with respect to x. To differentiate you must multiply the coefficient (number in front) by the power of x, then subtract 1 from the power. So here we find dy/dx = ...

3x² + 2x + 4

Starting with ∫a^x dx ,
We can re-write a^x using logs as e^ln(a)*x using some of their properties
We use the substitution u = ln(a)*x (as such du/dx = ln(a)) all...

You start by seperating the variables giving,

(1/x)*dx=(-6)*dt

you then integrate both sides with respect to the variables,

ln(x)=-6*t+c

you then subsitute in the given conditi...