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What is the value of $ rac{1- ext{cos} rac{ ext{Ï€}}{10}+i ext{sin} rac{ ext{Ï€}}{10}}{1- ext{cos} rac{ ext{Ï€}}{10}-i ext{sin} rac{ ext{Ï€}}{10}}$?
What is the simplified result of $ rac{1+ ext{cos} heta+i ext{sin} heta}{1+ ext{cos} heta-i ext{sin} heta}$?
If $(1+ ext{cos} heta+i ext{sin} heta) = ext{cos} heta+i ext{sin} heta$, what is the value of n?
Given $a= ext{√2}i$, which of the following is correct?
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What is the value of $(-i)^{1/3}$?
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Study Notes
Complex Numbers
- The value of $\frac{1-\cos\frac{\pi}{10}+i\sin\frac{\pi}{10}}{1-\cos\frac{\pi}{10}-i\sin\frac{\pi}{10}}$ is 1.
- The value of $\frac{1+cos\phi+isin\phi}{1+cos\phi-isin\phi}$ is $\cos\phi+isin\phi$.
- If $(1+\cos\theta+i\sin\theta) = \cos\theta+i\sin\theta$, then n is equal to 1.
- If $a=\sqrt{2}i$, then $a=-\sqrt{2}i$.
- The value of $(-i)^{1/3}$ is $-\frac{\sqrt{3}}{2}+i\frac{1}{2}$.
- $\cos\frac{\pi}{12}+i\sin\frac{\pi}{12}$ is a fourth root of $1+i\sqrt{3}$.
- $\left(\frac{1+i\sqrt{3}}{2}\right)^6+\left(\frac{1-i\sqrt{3}}{2}\right)^6$ is equal to 1.
- If $z = \frac{\sqrt{3}}{2}+i\frac{1}{2}$, then $Re(z)>0, Im(z)>0$.
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Description
Test your understanding of complex numbers and their properties with this quiz. Explore concepts such as Euler's formula, roots of unity, and transformations involving complex numbers. Perfect for students looking to enhance their skills in complex analysis!
