Polar Form of Complex Numbers - Video Tutorials & Practice Problems

Express the complex number $z=7+11i$ in polar form.

• A. $z=\sqrt{170}\left(\cos58\degree+i\sin58\degree\right)$
• B. $\sqrt{170}\left(\cos58\degree+\sin58\degree\right)$
• C. $z=\sqrt{170}+i58\degree$
• D. $z=170\left(\cos58\degree+i\sin58\degree\right)$

Express the complex number $z=2-4i$ in the polar form.

• A. $z=2\sqrt5\left(\sin297\degree+i\cos297\degree\right)$
• B. $z=2\sqrt5\left(\sin63\degree+i\cos63\degree\right)$
• C. $z=2\sqrt5\left(\cos297\degree+i\sin297\degree\right)$
• D. $z=2\sqrt5\left(\cos63\degree-i\sin63\degree\right)$

Express the complex number $z=1-\frac{\sqrt3}{3}i$ in polar form.

• A. $z=\frac{2\sqrt3}{3}\left(\cos\frac{\pi}{6}-i\sin\frac{\pi}{6}\right)$
• B. $z=\frac{2\sqrt3}{3}\left(\cos\frac{13\pi}{6}+i\sin\frac{13\pi}{6}\right)$
• C. $z=\frac{2}{\sqrt3}\left(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\right)$
• D. $z=\frac{2\sqrt3}{3}\left(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\right)$

Convert the complex number $z=12\left(\cos90\degree+i・\sin90\degree\right)$ from polar to rectangular form.

• A. $z=12i$
• B. $z=12$
• C. $z=1$
• D. $z=i$

Convert the complex number $z=\sqrt2\left(\cos\frac{7\pi}{4}+i・\sin\frac{7\pi}{4}\right)$ from polar to rectangular form.

• A. $z=\sqrt2-i\sqrt2$
• B. $z=1-i$
• C. $z=2-2i$
• D. $z=-i$