Exercises for Question Type 3: Converting complex numbers from Polar to Cartesian form

Question 1

Skill question

Express $6 (cos \frac{5 π}{4} + i sin \frac{5 π}{4})$ in Cartesian form.

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Question 2

Skill question

Express a complex number given in polar form into Cartesian form using exact trigonometric values for angles that are multiples of $\frac{π}{12}$ .

Express $5 (cos \frac{5 π}{12} + i sin \frac{5 π}{12})$ in Cartesian form, using exact surds.

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Question 3

Skill question

Express $12 (cos \frac{11 π}{6} + i sin \frac{11 π}{6})$ in Cartesian form.

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Question 4

Skill question

Convert $3.5 (cos \frac{5 π}{4} + i sin \frac{5 π}{4})$ into $a + bi$ form.

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Question 5

Skill question

Express $3 (cos \frac{π}{6} + i sin \frac{π}{6})$ in the form $a + bi$ .

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Question 6

Skill question

Express $7 (cos \frac{4 π}{3} + i sin \frac{4 π}{3})$ in Cartesian form.

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Question 7

Skill question

Convert $10 (cos \frac{3 π}{2} + i sin \frac{3 π}{2})$ into $a + bi$ form.

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Question 8

Skill question

Express $4 (cos \frac{π}{4} + i sin \frac{π}{4})$ in Cartesian form.

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Question 9

Skill question

Convert $5 (cos (- \frac{π}{3}) + i sin (- \frac{π}{3}))$ to Cartesian form.

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Question 10

Skill question

Convert $8 (cos \frac{2 π}{3} + i sin \frac{2 π}{3})$ to Cartesian form.

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Question 11

Skill question

Convert $5 (cos \frac{π}{3} + i sin \frac{π}{3})$ into Cartesian form.

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Question 12

Skill question

Express $23 (cos \frac{π}{6} + i sin \frac{π}{6})$ in Cartesian form.

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IB Mathematics Applications & Interpretation Question Type 3: Converting Complex Numbers from Polar to Cartesian Form Exercises