## Trigonometry (10th Edition)

$6i$
First, we use the product theorem to multiply the absolute values and add the arguments: $(\sqrt{6} cis 120^{\circ})(\sqrt{6} cis (-30^{\circ})) \\=\sqrt{6}\sqrt{6} cis (120^{\circ}-30^{\circ}) \\=6 cis (90^{\circ})$ Next, we change the expression into its equivalent form: $=6 cis (90^{\circ}) \\6(\cos90^{\circ}+i\sin90^{\circ})$ Since we know that $\cos90^{\circ}=0$ and $\sin90^{\circ}=1$, we substitute these values in the expression and simplify: $6(\cos90^{\circ}+i\sin90^{\circ}) \\=6(i) \\=6i$
The text passage describes a trigonometric calculation involving the multiplication of two complex numbers in polar form, followed by the conversion of the result to rectangular form.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Trigonometry (10th Edition)

$6i$
First, we use the product theorem to multiply the absolute values and add the arguments: $(\sqrt{6} cis 120^{\circ})(\sqrt{6} cis (-30^{\circ})) \\=\sqrt{6}\sqrt{6} cis (120^{\circ}-30^{\circ}) \\=6 cis (90^{\circ})$ Next, we change the expression into its equivalent form: $=6 cis (90^{\circ}) \\6(\cos90^{\circ}+i\sin90^{\circ})$ Since we know that $\cos90^{\circ}=0$ and $\sin90^{\circ}=1$, we substitute these values in the expression and simplify: $6(\cos90^{\circ}+i\sin90^{\circ}) \\=6(i) \\=6i$
user
The text passage describes a trigonometric calculation involving the multiplication of two complex numbers in polar form, followed by the conversion of the result to rectangular form.

TYPE: SINGLE_QUESTION_WITH_ANSWER