mathslover
Convert into polar form :
(1/2) + i ( \(\frac{\sqrt{3}}{2}\) )



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mathslover
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(1/2) + i ( \(\frac{\sqrt{3}}{2}\) )

mathslover
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I got : cos ( 4 pi/3 ) + sin ( 4 pi/3)

mathslover
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But the book says :
cos (  2pi/3 ) + i sin (  2pi/3). Which is also right...

Azteck
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isin

Azteck
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You're wrong.

mathslover
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Sorry typing mistake I meant i sin 4pi/3

mathslover
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^ cos ( 4 pi/3 ) + i sin(4pi/3)

Azteck
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Find the absolute value of this:
\[\left \frac{ 1 }{ 2 } \frac{ i \sqrt{3} }{ 2 }\right\]

mathslover
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So which should I prefer more ? 2pi/3 or 4 pi/3

Azteck
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So
\[=\sqrt{(\frac{ 1 }{ 2 })^2+(\frac{ \sqrt{3} }{ 2 })^2}\]

Azteck
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So r=1

Azteck
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Now draw it.

Azteck
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Drawing it gives you a way better picture of what the angle is.

mathslover
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\[\large{\sqrt{ (\frac{1}{2} )^2 + ( \frac { \sqrt{3}}{2})^2}}\]
right so it is : \(\1\)

Azteck
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dw:1359153193735:dw

Azteck
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You took the other angle

Azteck
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You go backwards meaning it will be negative.

mathslover
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By the diagram I think that the angle theta will surely lie in the III quadrant
i.e. 4 pi /3

mathslover
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Ok got it thanks.

Azteck
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If it's in the third of fourth quadrant go backwards.

Azteck
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third or fourth*