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Question 1 of 5: Simplify, write in polar form.
$$2\left(\text{cos}\frac{π}{4}+ i \hspace{.1em}\text{sin}\frac{π}{4}\right) \cdot 2\left(\text{cos}\frac{π}{6}+ i \hspace{.1em}\text{sin}\frac{π}{6}\right)$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$4\left(\text{cos}\frac{5π}{12}+ i \hspace{.1em}\text{sin}\frac{5π}{12}\right)$$
B
$$8\left(\text{cos}\frac{5π}{3}+ i \hspace{.1em}\text{sin}\frac{5π}{3}\right)$$
C
$$12\left(\text{cos}\frac{π}{6}+ i \hspace{.1em}\text{sin}\frac{π}{6}\right)$$
D
$$6\sqrt{17}\left(\text{cos}\frac{5π}{6}+ i \hspace{.1em}\text{sin}\frac{5π}{6}\right)$$
E
$$6\sqrt{17}\left(\text{cos}\frac{π}{4}+ i \hspace{.1em}\text{sin}\frac{π}{4}\right)$$
Question 2 of 5: Simplify, write in polar form.
$$6\left(\text{cos}\frac{3π}{4}+ i \hspace{.1em}\text{sin}\frac{3π}{4}\right) \cdot 5\left(\text{cos}\frac{7π}{6}+ i \hspace{.1em}\text{sin}\frac{7π}{6}\right)$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$4\left(\text{cos}\frac{19π}{12}+ i \hspace{.1em}\text{sin}\frac{19π}{12}\right)$$
B
$$2\sqrt{6}\left(\text{cos}\frac{7π}{6}+ i \hspace{.1em}\text{sin}\frac{7π}{6}\right)$$
C
$$30\left(\text{cos}\frac{23π}{12}+ i \hspace{.1em}\text{sin}\frac{23π}{12}\right)$$
D
$$6\sqrt{3}\left(\text{cos}\frac{23π}{12}+ i \hspace{.1em}\text{sin}\frac{23π}{12}\right)$$
E
$$\sqrt{2}\left(\text{cos}\frac{2π}{3}+ i \hspace{.1em}\text{sin}\frac{2π}{3}\right)$$
Question 3 of 5: Simplify, write in rectangular form.
$$2\sqrt{3}(\text{cos}\hspace{.1em}150° + i \hspace{.1em}\text{sin}\hspace{.1em}150°) \cdot 4 (\text{cos}\hspace{.1em}90° + i \hspace{.1em}\text{sin}\hspace{.1em}90°)$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$10\sqrt{3}+ 4i$$
B
$${-}9\sqrt{10}+ \frac{3}{4}i$$
C
$$3\sqrt{3}+ 3i$$
D
$${-4}\sqrt{3}- 12i$$
E
$$\frac{\sqrt{2}}{4}+ \frac{\sqrt{3}}{4}i$$
Question 4 of 5: Simplify, write in polar form.
$$\frac{4(\text{cos}\hspace{.1em}240° + i \hspace{.1em}\text{sin}\hspace{.1em}240°)}{5(\text{cos}\hspace{.1em}270° + i \hspace{.1em}\text{sin}\hspace{.1em}270°)}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\sqrt{26}(\text{cos}\hspace{.1em}240° + i \hspace{.1em}\text{sin}240°)$$
B
$$\sqrt{2}(\text{cos}\hspace{.1em}195° + i \hspace{.1em}\text{sin}195°)$$
C
$$\frac{6}{5}(\text{cos}\hspace{.1em}240° + i \hspace{.1em}\text{sin}240°)$$
D
$$\frac{\sqrt{2}}{5}(\text{cos}\hspace{.1em}330° + i \hspace{.1em}\text{sin}330°)$$
E
$$\frac{4}{5}(\text{cos}\hspace{.1em}330° + i \hspace{.1em}\text{sin}330°)$$
Question 5 of 5: Simplify, write in rectangular form.
$$\frac{\sqrt{21}(\text{cos}\hspace{.1em}150° + i \hspace{.1em}\text{sin}\hspace{.1em}150°)}{\sqrt{17}(\text{cos}\hspace{.1em}90° + i \hspace{.1em}\text{sin}\hspace{.1em}90°)}$$
Finish »
Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{\sqrt{3}}{4}+ \frac{1}{4}i$$
B
$$i$$
C
$$\frac{\sqrt{357}}{34}+ \frac{3\sqrt{119}}{34}i$$
D
$$\sqrt{34}+ 8i$$
E
$$\frac{\sqrt{22}}{12}- \frac{\sqrt{66}}{12}i$$

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