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
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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.)
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.