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Zurtex

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I'm like writing my homework out on a computer and find LateX the easiest code to use (I have a fairly easy one at home but at college their maths editors are very limited)

I was going to use the preview post function to copy and paste everything into word but unfortunately it just stays the same no matter what I do (stuck on my first preview post). I am going to use and edit this thread for my homework but could someone please give a link of an online system where I can input LateX code and get a visual display of it.

1a) [tex]{ \left[ \cos{ \frac{2 \pi}{5}} +i\sin{ \frac{2 \pi}{5}} \right] }^{10}[/tex]

[tex]\cos{4\pi} + i\sin{4\pi} = 1[/tex]

b) [tex] { \left[ \cos{\frac{\pi}{12}} + i\sin{\frac{\pi}{12}} \right] }^8 [/tex]

[tex] \cos{\frac{3\pi}{4}} + i\sin{\frac{3\pi}{4}} = \frac{\sqrt{2}}{2} + \frac{i\sqrt{2}}{2}[/tex]

c) [tex] {\left[ \cos{\left(-\frac{\pi}{27}\right)} + i\sin{\left(-\frac{\pi}{27}\right)} \right]}^9 [/tex]

[tex] \cos{\left(-\frac{\pi}{3}\right)} + i\sin{\left(-\frac{\pi}{3}\right)} = \frac{1}{2} - \frac{\sqrt{3}}{2} [/tex]

d) [tex] {\left( \cos{\frac{\pi}{18}} - i\sin{\frac{\pi}{18}} \right)}^3[/tex]

[tex] {\left( \cos{\left[-\frac{\pi}{18} \right]} + i\sin{\left[-\frac{\pi}{18}\right]} \right)}^3[/tex]

[tex] \cos{\left[-\frac{\pi}{6}\right]} + i\sin{\left[-\frac{\pi}{6}\right]} = \frac{\sqrt{3}}{2} + \frac{i}{2}[/tex]

2) [tex] z = 2(1 - i\sqrt{3}) [/tex]

[tex] z = 2 - i2\sqrt{3} [/tex]

[tex] |z| = 4 [/tex]

[tex] arg(z) = -\frac{\pi}{3} [/tex]

[tex]z^8 = \left[ 4 \left( \cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}} \right) \right]^8 [/tex]

[tex] z^8 = 4^8 \left( \cos{\frac{8\pi}{3}} + i\sin{\frac{8\pi}{3}} \right) [/tex]

[tex] z^8 = 65536 \left( -\frac{1}{2} + \frac{i\sqrt{3}}{2} \right) [/tex]

[tex] z^8 = -16384 + i16384\sqrt{3} [/tex]

[tex] \frac{1}{z^5} = z^{-5} [/tex]

[tex] z^{-5} = \left[ 4 \left( \cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}} \right) \right]^{-5} [/tex]

[tex] z^{-5} = 4^{-5} \left( \cos{\frac{-5\pi}{3}} + i\sin{\frac{-5\pi}{3}} \right) [/tex]

[tex] z^{-5} = \frac{1}{1024} \left( \frac{1}{2} + \frac{i\sqrt{3}}{2} \right) [/tex]

[tex]z^{-5} = \frac{1}{2048} + \frac{i\sqrt{3}}{2048}[/tex]

I was going to use the preview post function to copy and paste everything into word but unfortunately it just stays the same no matter what I do (stuck on my first preview post). I am going to use and edit this thread for my homework but could someone please give a link of an online system where I can input LateX code and get a visual display of it.

1a) [tex]{ \left[ \cos{ \frac{2 \pi}{5}} +i\sin{ \frac{2 \pi}{5}} \right] }^{10}[/tex]

[tex]\cos{4\pi} + i\sin{4\pi} = 1[/tex]

b) [tex] { \left[ \cos{\frac{\pi}{12}} + i\sin{\frac{\pi}{12}} \right] }^8 [/tex]

[tex] \cos{\frac{3\pi}{4}} + i\sin{\frac{3\pi}{4}} = \frac{\sqrt{2}}{2} + \frac{i\sqrt{2}}{2}[/tex]

c) [tex] {\left[ \cos{\left(-\frac{\pi}{27}\right)} + i\sin{\left(-\frac{\pi}{27}\right)} \right]}^9 [/tex]

[tex] \cos{\left(-\frac{\pi}{3}\right)} + i\sin{\left(-\frac{\pi}{3}\right)} = \frac{1}{2} - \frac{\sqrt{3}}{2} [/tex]

d) [tex] {\left( \cos{\frac{\pi}{18}} - i\sin{\frac{\pi}{18}} \right)}^3[/tex]

[tex] {\left( \cos{\left[-\frac{\pi}{18} \right]} + i\sin{\left[-\frac{\pi}{18}\right]} \right)}^3[/tex]

[tex] \cos{\left[-\frac{\pi}{6}\right]} + i\sin{\left[-\frac{\pi}{6}\right]} = \frac{\sqrt{3}}{2} + \frac{i}{2}[/tex]

2) [tex] z = 2(1 - i\sqrt{3}) [/tex]

[tex] z = 2 - i2\sqrt{3} [/tex]

[tex] |z| = 4 [/tex]

[tex] arg(z) = -\frac{\pi}{3} [/tex]

[tex]z^8 = \left[ 4 \left( \cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}} \right) \right]^8 [/tex]

[tex] z^8 = 4^8 \left( \cos{\frac{8\pi}{3}} + i\sin{\frac{8\pi}{3}} \right) [/tex]

[tex] z^8 = 65536 \left( -\frac{1}{2} + \frac{i\sqrt{3}}{2} \right) [/tex]

[tex] z^8 = -16384 + i16384\sqrt{3} [/tex]

[tex] \frac{1}{z^5} = z^{-5} [/tex]

[tex] z^{-5} = \left[ 4 \left( \cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}} \right) \right]^{-5} [/tex]

[tex] z^{-5} = 4^{-5} \left( \cos{\frac{-5\pi}{3}} + i\sin{\frac{-5\pi}{3}} \right) [/tex]

[tex] z^{-5} = \frac{1}{1024} \left( \frac{1}{2} + \frac{i\sqrt{3}}{2} \right) [/tex]

[tex]z^{-5} = \frac{1}{2048} + \frac{i\sqrt{3}}{2048}[/tex]

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