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

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!