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In this lesson, we will learn how to convert the different forms of the complex number (algebraic, trigonometric, and exponential forms).

Q1:

Put π§ = 4 β 3 οΌ 5 π 6 β π 5 π 6 ο c o s s i n in exponential form.

Q2:

Put π§ = β 4 β 3 οΌ 5 π 6 + π 5 π 6 ο s i n c o s in exponential form.

Q3:

Express the complex number π = π β 4 β π 2 3 π 1 2 in exponential form.

Q4:

Given that π§ = β 3 2 β 3 2 π , find π§ 5 , giving your answer in exponential form.

Q5:

Given that π = 1 1 ( 3 1 5 + π 3 1 5 ) c o s s i n β β , express π in algebraic form.

Q6:

Given that π = 5 [ ( β 3 3 0 ) + π ( β 3 3 0 ) ] c o s s i n β β , express π in algebraic form.

Q7:

Put π§ = 6 ο» β π 4 + π π 4 ο c o s s i n in exponential form.

Q8:

Given that π = 6 [ π + π π ] c o s s i n , find the algebraic form of π .

Q9:

Given that π = 6 β 2 β 6 β 2 π , write π in trigonometric form.

Q10:

Express the number β 3 π in trigonometric form.

Q11:

Express the number β 1 + π in trigonometric form.

Q12:

Simplify π§ = 4 β 3 π + 4 β 3 π + 3 β 3 + οΉ 5 π + 6 π + 6 π ο π 4 5 3 2 , giving your answer in algebraic form, and hence express the square roots of π§ in exponential form.

Q13:

Put π§ = 3 β 2 ο» β π 4 + π π 4 ο s i n c o s in exponential form.

Q14:

Which of the following expresses the complex number π in polar coordinates?

Q15:

Given that π = 5 β 2 2 β 5 β 2 2 π , find the trigonometric form of 1 π .

Q16:

Simplify ( β 1 β π ) 6 , giving your answer in trigonometric form.

Q17:

Put β 8 2 + 2 β 3 π in the form π₯ + π¦ π , where π₯ , π¦ β β , and then write it in trigonometric form.

Q18:

Put π§ = β 7 ο» π 4 + π π 4 ο c o s s i n in exponential form.

Q19:

Express the complex number π = 1 4 4 3 β 3 + 3 π in trigonometric form.

Q20:

Simplify β 8 + 4 β 3 π 5 + β 3 π , giving your answer in both algebraic and trigonometric form.

Q21:

Determine the real part of a complex number whose modulus is 4 β 3 and principal amplitude is 5 π 6 .

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