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Express 6 in the exponential form of (6*exp(2πin)), where n is an integertake the fourth root of this, remembering that taking the fourth root is taking to the power of 1/4, and by rules of indices the expre...

Firstly, I haven't seen the notation I used in alevel but I just used it for the sake of ease of typing it online.1st. Sub in the trial solution f(x)= Ae^(mx) and its derivatives- f'(x)= Ame^(mx) and f''(x)=...

Rewrite as arg(z-5) - arg(z-3) = π/6 and let arg(z-5) = b and arg(z-3) = a, so that b-a = π/6Since we know that each argument makes a half line (starting at (3,0) for angle a, (5,0) for angle b) the half lin...

1st we note our three methods for solving 1st order differential equation: separating the x and y variables to both sides of the equation, and integrating both sides with respect to x. Recognising an exact d...

To simplify this question, it is possible to expand the two elements of the function and then add the two expansions together.First, the expansion of sin(3x) around the origin is sin(3 0)+d/dx sin(3x)+d²/dx²...