How do you simplify $\frac{1}{2} (cos (\frac{π}{3}) + i sin (\frac{π}{3})) \div 3 (cos (\frac{π}{6}) + i sin g (\frac{π}{6}))$ $1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))$ and express the result in rectangular form?

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How do you simplify $\frac{1}{2} (cos (\frac{π}{3}) + i sin (\frac{π}{3})) \div 3 (cos (\frac{π}{6}) + i sin g (\frac{π}{6}))$ $1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))$ and express the result in rectangular form?

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Answer 1 · 2017-02-16T03:28:55

$\frac{1}{6} i$ $1/6 i$

Explanation:

Using Euler's formula,

$cos θ + i sin θ = e^{i θ}$ $cos theta +i sin theta = e^(i theta)$ , the given problem reduces to,
$\frac{\frac{1}{2} e^{i \frac{π}{3}}}{3 e^{i \frac{π}{6}}}$ $(1/2 e^(i pi/3)) / (3 e^(i pi/6)$

$\frac{1}{6} e^{i} (\frac{π}{3} - \frac{π}{6})$ $1/6 e^i( pi/3 -pi/6)$

$\frac{1}{6} e^{i \frac{π}{2}}$ $1/6 e^(i pi/2)$

$\frac{1}{6} (cos (\frac{π}{2}) + i sin (\frac{π}{2}))$ $1/6 (cos (pi/2) +i sin (pi/2))$

$\frac{1}{6} i$ $1/6 i$ ....................... [ $cos (\frac{π}{2}) = 0 and sin (\frac{π}{2}) = 1$ $cos (pi/2) =0 and sin (pi/2) =1$ ]

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How do you simplify $\frac{1}{2} (cos (\frac{π}{3}) + i sin (\frac{π}{3})) \div 3 (cos (\frac{π}{6}) + i sin g (\frac{π}{6}))$ $1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))$ and express the result in rectangular form?

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Explanation:

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How do you simplify 1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))12(cos(π3)+isin(π3))÷3(cos(π6)+ising(π6))1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6)) and express the result in rectangular form?

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Explanation:

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How do you simplify $\frac{1}{2} (cos (\frac{π}{3}) + i sin (\frac{π}{3})) \div 3 (cos (\frac{π}{6}) + i sin g (\frac{π}{6}))$ $1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))$ and express the result in rectangular form?