Operations with Complex Numbers in Polar Form

Submitted by vladimir.arzt on Thu, 05/23/2024 - 18:18

Project ID:

7200000042

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Question:

Let

a

b

, and

c

be complex numbers, where:

\begin{aligned} a & = 4 (\cos \frac{7 π}{6} + i \sin \frac{7 π}{6}), \\ b & = \cos \frac{5 π}{6} + i \sin \frac{5 π}{6}, \\ c & = 2 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3}) . \end{aligned}

Match the given complex expressions with their corresponding values expressed in polar form.

Questions Title:

Expression with complex numbers

Answers Title:

Value in polar form

Question 1:

\frac{a}{b}

Answer 1:

4 (\cos \frac{π}{3} + i \sin \frac{π}{3})

Question 2:

c^{2}

Answer 2:

4 (\cos \frac{4 π}{3} + i \sin \frac{4 π}{3})

Question 3:

b \cdot c

Answer 3:

2 (\cos \frac{3 π}{2} + i \sin \frac{3 π}{2})

Question 4:

\frac{a \cdot c}{b}

Answer 4:

8 (\cos π + i \sin π)

Question 5:

{(\frac{a \cdot b}{c})}^{2}

Answer 5:

$4 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3})$

Question 6:

\frac{a^{3} \cdot b}{c^{4}}

Answer 6:

4 (\cos \frac{5 π}{3} + i \sin \frac{5 π}{3})

Answer 7:

2 (\cos \frac{4 π}{3} + i \sin \frac{4 π}{3})

Answer 8:

8 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3})

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