Complex Numbers Quiz

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 $Re(z)>0, Im(z)>0$.