text: ### Home > PC > Chapter 11 > Lesson 11.2.1 > Problem11-71
  
  11-71.
  1. Find the rectangular form of each complex number. Use exact values! Homework Help ✎
  
  1. z = 6 (cos() + i sin())
  
  2. z = 7 (cos() + i sin())
  
  Substitute the exact values for sine and cosine of 5π/6.
  
  $\textit{z}=6\left( -\frac{\sqrt{3}}{2}+\frac{1}{2}\textit{i} \right)$
  
  Distribute.
  
  $\textit{z}=-3\sqrt{3}+3\textit{i}$
  
  Recall how you graph complex numbers.Where would this point be in the xy-plane?
  
  $\left( -3\sqrt{3},3 \right)$
explanation: The document contains a math problem with a question and an answer. The question asks to find the rectangular form of a given complex number, and the answer is provided, showing the steps to convert the complex number from polar to rectangular form.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ### Home > PC > Chapter 11 > Lesson 11.2.1 > Problem11-71
  
  11-71.
  1. Find the rectangular form of each complex number. Use exact values! Homework Help ✎
  
  1. z = 6 (cos() + i sin())
  
  2. z = 7 (cos() + i sin())
  
  Substitute the exact values for sine and cosine of 5π/6.
  
  $\textit{z}=6\left( -\frac{\sqrt{3}}{2}+\frac{1}{2}\textit{i} \right)$
  
  Distribute.
  
  $\textit{z}=-3\sqrt{3}+3\textit{i}$
  
  Recall how you graph complex numbers.Where would this point be in the xy-plane?
  
  $\left( -3\sqrt{3},3 \right)$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem with a question and an answer. The question asks to find the rectangular form of a given complex number, and the answer is provided, showing the steps to convert the complex number from polar to rectangular form.
  
  Label: question-and-answer