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

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

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Question 1

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

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

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

Compute \frac{3 ( c o s \frac{π}{4} + i s i n \frac{π}{4} ) \times 4 ( c o s \frac{π}{3} + i s i n \frac{π}{3} )}{2 ( c o s \frac{π}{6} + i s i n \frac{π}{6} )} and express the answer in polar form.

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Question 5

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

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

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

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

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

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

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

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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