Math Problem Statement
Write the expression in rectangular form, x plus y i, and in exponential form, r e Superscript i theta. left bracket 3 left parenthesis cosine StartFraction pi Over 10 EndFraction plus i sine StartFraction pi Over 10 EndFraction right parenthesis right bracket Superscript 5 Question content area bottom Part 1 The rectangular form of the given expression is enter your response here, and the exponential form of the given expression is enter your response here. (Simplify your answers. Type exact answers, using pi as needed. Use integers or fractions for any numbers in the expressions.)
Solution
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Polar Form
Rectangular Form
Exponential Form
De Moivre's Theorem
Formulas
De Moivre's Theorem: (r (cos(θ) + i sin(θ)))^n = r^n (cos(nθ) + i sin(nθ))
Exponential Form: re^(iθ)
Theorems
De Moivre's Theorem
Suitable Grade Level
Grades 11-12
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