8.5 Polar form of complex numbers  (Page 4/8)

A complex number is $a+bi.$ Explain each part.

What does the absolute value of a complex number represent?

How is a complex number converted to polar form?

How do we find the product of two complex numbers?

What is De Moivre’s Theorem and what is it used for?

$5+\text{}3i$

$-7+\text{}i$

$-3-3i$

$\sqrt{2}-6i$

$2i$

$2.2-3.1i$

$2+2i$

$8-4i$

$-\frac{1}{2}-\frac{1}{2}\text{}i$

$\sqrt{3}+i$

$3i$

$z=7\mathrm{cis}\left(\frac{\pi }{6}\right)$

$z=2\mathrm{cis}\left(\frac{\pi }{3}\right)$

$z=4\mathrm{cis}\left(\frac{7\pi }{6}\right)$

$z=7\mathrm{cis}\left(\mathrm{25°}\right)$

$z=3\mathrm{cis}\left(\mathrm{240°}\right)$

$z=\sqrt{2}\mathrm{cis}\left(\mathrm{100°}\right)$

$z_1=2\sqrt{3}\mathrm{cis}\left(\mathrm{116°}\right);z_2=2\mathrm{cis}\left(\mathrm{82°}\right)$

$z_1=\sqrt{2}\mathrm{cis}\left(\mathrm{205°}\right);z_2=2\sqrt{2}\mathrm{cis}\left(\mathrm{118°}\right)$

$z_1=3\mathrm{cis}\left(\mathrm{120°}\right);z_2=\frac{1}{4}\mathrm{cis}\left(\mathrm{60°}\right)$

$z_1=3\mathrm{cis}\left(\frac{\pi }{4}\right);z_2=5\mathrm{cis}\left(\frac{\pi }{6}\right)$

$z_1=\sqrt{5}\mathrm{cis}\left(\frac{5\pi }{8}\right);z_2=\sqrt{15}\mathrm{cis}\left(\frac{\pi }{12}\right)$

$z_1=4\mathrm{cis}\left(\frac{\pi }{2}\right);z_2=2\mathrm{cis}\left(\frac{\pi }{4}\right)$

$z_1=21\mathrm{cis}\left(\mathrm{135°}\right);z_2=3\mathrm{cis}\left(\mathrm{65°}\right)$

$z_1=\sqrt{2}\mathrm{cis}\left(\mathrm{90°}\right);z_2=2\mathrm{cis}\left(\mathrm{60°}\right)$

$z_1=15\mathrm{cis}\left(\mathrm{120°}\right);z_2=3\mathrm{cis}\left(\mathrm{40°}\right)$

$z_1=6\mathrm{cis}\left(\frac{\pi }{3}\right);z_2=2\mathrm{cis}\left(\frac{\pi }{4}\right)$

$z_1=5\sqrt{2}\mathrm{cis}\left(\pi \right);z_2=\sqrt{2}\mathrm{cis}\left(\frac{2\pi }{3}\right)$

$z_1=2\mathrm{cis}\left(\frac{3\pi }{5}\right);z_2=3\mathrm{cis}\left(\frac{\pi }{4}\right)$

Find $z^3$ when $z=5\mathrm{cis}\left(\mathrm{45°}\right).$

Find $z^4$ when $z=2\mathrm{cis}\left(\mathrm{70°}\right).$

Find $z^2$ when $z=3\mathrm{cis}\left(\mathrm{120°}\right).$

Find $z^2$ when $z=4\mathrm{cis}\left(\frac{\pi }{4}\right).$

Find $z^4$ when $z=\mathrm{cis}\left(\frac{3\pi }{16}\right).$

Find $z^3$ when $z=3\mathrm{cis}\left(\frac{5\pi }{3}\right).$

Evaluate the cube root of $z$ when $z=27\mathrm{cis}\left(\mathrm{240°}\right).$

Evaluate the square root of $z$ when $z=16\mathrm{cis}\left(\mathrm{100°}\right).$

Evaluate the cube root of $z$ when $z=32\mathrm{cis}\left(\frac{2\pi }{3}\right).$

Evaluate the square root of $z$ when $z=32\text{cis}\left(\pi \right).$

Evaluate the cube root of $z$ when $z=8\mathrm{cis}\left(\frac{7\pi }{4}\right).$

$2+4i$

$-3-3i$

$5-4i$

$-1-5i$

$3+2i$

$2i$

$-4$

$6-2i$

$-2+i$

$1-4i$

Use the rectangular to polar feature on the graphing calculator to change $5+5i$ to polar form.

Use the rectangular to polar feature on the graphing calculator to change $3-2i$ to polar form.

Use the rectangular to polar feature on the graphing calculator to change $-3-8i$ to polar form.

Use the polar to rectangular feature on the graphing calculator to change $4\mathrm{cis}\left(\mathrm{120°}\right)$ to rectangular form.

Use the polar to rectangular feature on the graphing calculator to change $2\mathrm{cis}\left(\mathrm{45°}\right)$ to rectangular form.

Use the polar to rectangular feature on the graphing calculator to change $5\mathrm{cis}\left(\mathrm{210°}\right)$ to rectangular form.