Write the complex number in the rectangular form.

Question

0.7 left parenthesis cosine StartFraction 5 pi Over 9 EndFraction plus i sine StartFraction 5 pi Over 9 EndFraction right parenthesis
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Part 1
0.7 left parenthesis cosine StartFraction 5 pi Over 9 EndFraction plus i sine StartFraction 5 pi Over 9 EndFraction right parenthesis
equals
  
enter your response here
​(Simplify your answer. Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to the nearest thousandth as​ needed.)Write the complex number in the rectangular form.
0.7 left parenthesis cosine StartFraction 5 pi Over 9 EndFraction plus i sine StartFraction 5 pi Over 9 EndFraction right parenthesis
Question content area bottom
Part 1
0.7 left parenthesis cosine StartFraction 5 pi Over 9 EndFraction plus i sine StartFraction 5 pi Over 9 EndFraction right parenthesis
equals
  
enter your response here
​(Simplify your answer. Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to the nearest thousandth as​ needed.)

Answer 1

To convert the given complex number from polar form to rectangular form, we can use Euler's formula:

0.7(cos(5π/9) + i sin(5π/9))

This simplifies to:

0.7(0.309 + 0.951i)

Multiplying out gives:

0.7(0.309) + 0.7(0.951)i

0.2163 + 0.6657i

Therefore, the complex number in rectangular form is approximately 0.216 + 0.666i.