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In this lesson, we will learn how to represent a complex number in polar form, calculate the modulus and argument, and use this to change the form of a complex number.

Q1:

Find the trigonometric form of the complex number π represented by the given Argand diagram.

Q2:

Given that π§ = 1 1 and π§ = ( 3 π + π 3 π ) 2 2 c o s s i n , find the trigonometric form of π§ π§ 1 2 .

Q3:

Express 1 2 ο οΌ 5 π 6 ο + π οΌ 5 π 6 ο ο c o s s i n in algebraic form.

Q4:

Find the modulus of the complex number 1 + π .

Find the argument of the complex number 1 + π .

Hence, write the complex number 1 + π in polar form.

Q5:

Consider the diagram.

Which of the following correctly describes the relationship between π , π , and π ?

Which of the following correctly describes the relationship between π , π , and π ?

Hence, express π§ in terms of π and π .

Q6:

The Argand diagram shows the complex number π§ .

Write π§ in rectangular form.

Convert π§ to polar form, rounding the argument to two decimal places.

Q7:

Express the complex number π = 4 π in trigonometric form.

Q8:

Given that π = β 3 + π , determine the trigonometric form of π .

Q9:

If π = π ( π + π π ) c o s s i n , what is 1 π ?

Q10:

Simplify 6 β 6 π β 2 π , giving your answer in both algebraic and trigonometric form.

Q11:

Simplify β 5 + 5 β 3 π β β 3 β π , giving your answer in both algebraic and trigonometric form.

Q12:

Given that π β 2 = ( π + 2 ) π , determine the trigonometric form of the complex number π .

Q13:

Given that π = ( 6 π β 6 ) ( 4 + 3 π ) ( 1 + 2 π ) 2 , express the complex number π in the form of π₯ + π¦ π , and then determine its trigonometric form.

Q14:

Determine, in trigonometric form, the square roots of ο½ β 5 β 5 π β 5 + 5 π ο 9 .

Q15:

Simplify β 7 + 4 β 3 + ο» β 7 β 3 β 4 ο π 7 + 4 π , giving your answer in both algebraic and trigonometric form.

Q16:

Given that | π | = 9 and the argument of π is π = π 6 , find π , giving your answer in trigonometric form.

Q17:

Given that | π | = 8 and the argument of π is π = 3 6 0 β , find π , giving your answer in trigonometric form.

Q18:

Given that | π | = 5 and the argument of π is π = 2 π + 2 π π , where π β β€ , find π , giving your answer in trigonometric form.

Q19:

Given that | π | = 3 and the argument of π is π = π 3 , find π , giving your answer in algebraic form.

Q20:

Given that | π | = 1 2 and the argument of π is π = 1 2 0 β , find π , giving your answer in algebraic form.

Q21:

Given that | π§ | = 5 and the argument of π§ is π = 2 7 0 β , find π§ , giving your answer in algebraic form.

Q22:

Given that π = 7 [ ( β 5 8 ) + π ( β 5 8 ) ] c o s s i n β β , determine the algebraic form of π , approximating the real and imaginary parts to the nearest two decimal places.

Q23:

Given that , find the principal argument of , where .

Q24:

Find c o s π 6 .

Find s i n π 6 .

Hence, express the complex number 1 0 ο» π 6 + π π 6 ο c o s s i n in rectangular form.

Q25:

Given that π§ = 1 3 ( 3 0 + π 3 0 ) c o s s i n β β , find 1 π§ .

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