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In this lesson, we will learn how to perform basic operations on complex numbers in different forms.

Q1:

Express β 6 ο» ο» π 6 ο + π ο» π 6 ο ο Γ β 1 0 ο» ο» π 2 ο + π ο» π 2 ο ο c o s s i n c o s s i n in the form π₯ + π¦ π .

Q2:

Given that π = οΌ 2 π 3 ο + π οΌ 2 π 3 ο c o s s i n , express π β 1 in exponential form.

Q3:

Given that π§ = 8 ( 2 4 0 + π 2 4 0 ) 1 β β c o s s i n , π§ = 4 οΌ 5 π 4 + π 5 π 4 ο 2 c o s s i n , and π§ = 8 ( 4 5 + π 4 5 ) 3 β β c o s s i n , find π§ π§ π§ 1 6 2 4 3 , giving your answer in exponential form.

Q4:

Given that and , determine .

Q5:

If π§ = 3 ( 4 5 + π 4 5 ) c o s s i n β β , what is π§ 2 ?

Q6:

Given that π = 8 οΌ οΌ 1 9 π 1 2 ο β π οΌ 1 9 π 1 2 ο ο 1 2 c o s s i n and π = 3 π 2 π 1 1 π 6 , where π = β 1 2 , express π = π π 1 2 2 in trigonometric form.

Q7:

Given that and , find in trigonometric form.

Q8:

Express 6 π Γ· 2 π 3 π 2 4 π 3 π π in exponential and trigonometric forms.

Q9:

Put 8 + 8 β 3 π 1 6 ο» ο» β ο + π ο» β ο ο c o s s i n π 2 π 2 in the form π₯ + π¦ π , where π₯ , π¦ β β , and then express it in trigonometric form.

Q10:

Simplify π = 5 οΌ οΌ 3 π 4 ο + π οΌ 3 π 4 ο ο Γ 1 2 π c o s s i n 1 3 π 1 2 π , giving your answer in algebraic form.

Q11:

Simplify π = 1 0 ο» ο» π 2 ο + π ο» π 2 ο ο Γ 7 π c o s s i n 2 π 3 π , giving your answer in algebraic form.

Q12:

Given that π = 1 8 β 1 8 π 1 and π = οΌ 7 π 6 ο β π οΌ 7 π 6 ο 2 c o s s i n , find π π 1 2 , giving your answer in exponential form.

Q13:

Express 4 β 7 π Γ β 7 π 2 π Γ 7 π 3 π 4 7 π 6 1 1 π 1 2 π 3 π π π π in exponential and trigonometric forms.

Q14:

Put ο» + π ο ο» + π ο ο» + π ο c o s s i n c o s s i n c o s s i n π 3 π 3 3 3 π 2 3 π 2 2 π 3 π 3 2 in the form π + π π .

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