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