The first one, integration, I just want to check my answer.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int \frac{1}{64} (\cos6\theta + 6\cos4\theta + 15\cos2\theta + 20) = \frac{1}{64} (\frac{\sin6\theta}{6} + \frac{6\sin4\theta}{4} + \frac{15\sin2\theta}{2} + 20\theta + c[/tex]

I just wasn't sure if the integral of a constant wrt theta was constant*theta.

The complex roots question:

[tex]z^5 - i = (z-w1)(z-w2)(z-w3)(z-w4)(z-w5) = 0[/tex]

Show that w1 + w2 + w3 + w4 + w5 = 0

From what our lecturer told us, [tex]-\prod_{1}[/tex] = 0 so the sum of the roots = 0. I don't really understand this though

The radians problem... is basically because I don't know how to express radian in decimals into pi radians. [As part of an answer for coshz = 2i] I want to express the argument of [tex]2 \pm \sqrt{5}[/tex] which would be [tex]\tan^{-1} \sqrt{5}/2[/tex].

In case you want to know, I found [tex]z = log(2 \pm i\sqrt{5}) = ln|2 \pm i\sqrt{5}| + i arg(2 \pm i\sqrt{5})[/tex]

I just need help finishing up the question :)

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# Homework Help: Integration, complex roots and radians

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