1.13 Complex numbers: polar and exponential forms Quiz

1. Find $|3-4i|$.

• A. $3$
• B. $5$
• C. $7$
• D. $25$

2. What is $2e^{\frac{\pi}{2}i}$ in the form $a+bi$?

• A. $2$
• B. $-2i$
• C. $2i$
• D. $i$

3. Find $\left(2e^{\frac{\pi}{6}i}\right)^3$.

• A. $8e^{\frac{\pi}{2}i}$
• B. $6e^{\frac{\pi}{2}i}$
• C. $8e^{\frac{\pi}{18}i}$
• D. $2e^{\frac{\pi}{2}i}$

4. What does multiplying $z$ by $3e^{\frac{\pi}{3}i}$ do on the Argand diagram?

• A. Stretches by $\frac13$ and rotates $3$ radians
• B. Translates $z$ by $3$ units
• C. Rotates by $3$ radians with no stretch
• D. Stretches by scale factor $3$ and rotates $\frac{\pi}{3}$ anticlockwise

5. Find the principal argument of $-2-2i$.

• A. $\frac{3\pi}{4}$
• B. $-\frac{3\pi}{4}$
• C. $\frac{\pi}{4}$
• D. $-\frac{\pi}{4}$