Exercises for Question Type 5: Applying multiplication and division to complex numbers in polar form

Question 1

Skill question

Find the value of $(\frac{9 ( cos \frac{4 π}{5} + i sin \frac{4 π}{5} )}{3 ( cos \frac{7 π}{10} + i sin \frac{7 π}{10} )}) \times 2 (cos \frac{π}{10} + i sin \frac{π}{10})$ giving your answer in polar form.

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Question 2

Skill question

Find the product of three complex numbers in polar form: $2 (cos \frac{π}{8} + i sin \frac{π}{8}) \times 3 (cos \frac{π}{4} + i sin \frac{π}{4}) \times 5 (cos \frac{π}{16} + i sin \frac{π}{16}) .$

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Question 3

Skill question

Divide $8 (cos \frac{5 π}{12} + i sin \frac{5 π}{12})$ by $2 (cos \frac{π}{6} + i sin \frac{π}{6})$ and express the result in polar form.

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Question 4

Skill question

Compute $\frac{3 ( cos \frac{π}{4} + i sin \frac{π}{4} ) \times 4 ( cos \frac{π}{3} + i sin \frac{π}{3} )}{2 ( cos \frac{π}{6} + i sin \frac{π}{6} )}$ and express the answer in polar form.

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Question 5

Skill question

Compute the product $5 (cos \frac{π}{5} + i sin \frac{π}{5}) \times 5 (cos \frac{2 π}{5} + i sin \frac{2 π}{5})$ and give the answer in polar form.

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Question 6

Skill question

Divide $10 (cos \frac{13 π}{12} + i sin \frac{13 π}{12})$ by $5 (cos \frac{7 π}{12} + i sin \frac{7 π}{12})$ and express the result in polar form.

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Question 7

Skill question

Express the quotient $\frac{8 e ^{i \frac{3 π}{7}}}{4 e ^{i \frac{5 π}{14}}}$ in the form $r e^{i θ}$ .

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Question 8

Skill question

Compute the product $4 (cos \frac{2 π}{3} + i sin \frac{2 π}{3}) \times 6 (cos \frac{5 π}{6} + i sin \frac{5 π}{6})$ and give the answer in polar form.

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Question 9

Skill question

Express $\frac{5 e ^{i \frac{π}{5}} \times 2 e ^{i \frac{3 π}{10}}}{3 e ^{i \frac{π}{2}}}$ in the form $R e^{i θ}$ .

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Question 10

Skill question

Evaluate $\frac{12 ( cos \frac{11 π}{12} + i sin \frac{11 π}{12} ) \times 5 ( cos \frac{π}{3} + i sin \frac{π}{3} )}{6 ( cos \frac{5 π}{12} + i sin \frac{5 π}{12} )}$ and express the answer in polar form.

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Question 11

Skill question

Multiplication of Complex Numbers in Polar Form

Multiply the complex numbers $5 (cos \frac{π}{16} + i sin \frac{π}{16})$ and $3 (cos \frac{3 π}{16} + i sin \frac{3 π}{16})$ and express the answer in polar form.

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Question 12

Skill question

Find the product $7 (cos \frac{7 π}{8} + i sin \frac{7 π}{8}) \times 2 (cos \frac{9 π}{8} + i sin \frac{9 π}{8})$ in polar form.

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IB Mathematics Applications & Interpretation Question Type 5: Applying Multiplication and Division to Complex Numbers in Polar Form Exercises

Multiplication of Complex Numbers in Polar Form