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In this lesson, we will learn how to perform calculations with complex numbers in polar form.

Q1:

Given that π§ = 2 0 ο» π 2 + π π 2 ο 1 c o s s i n and π§ = 4 ο» π 6 + π π 6 ο 2 c o s s i n , find π§ π§ 1 2 in polar form.

Q2:

Given that π§ = 7 ( 3 1 5 + π 3 1 5 ) s i n c o s β β , find π§ 2 , giving your answer in exponential form.

Q3:

Given that π§ = 3 β 2 ( 2 2 5 β π 2 2 5 ) c o s s i n β β , find π§ 2 , giving your answer in exponential form.

Q4:

Given that π§ = 2 ( 9 0 β π 9 0 ) 1 β β c o s s i n and π§ = 4 ( 3 0 + π 3 0 ) 2 β β s i n c o s , find π§ π§ 1 2 , giving your answer in exponential form.

Q5:

If π = 7 ( π + π π ) 1 1 1 c o s s i n , π = 1 6 ( π + π π ) 2 2 2 c o s s i n , and π + π = π 1 2 , then what is π π 1 2 ?

Q6:

Given that π§ = 1 6 ( 4 5 + π 4 5 ) 1 β β 2 c o s s i n and π§ = 2 ( β 2 8 5 β π 2 8 5 ) 2 β β 2 s i n c o s , find π§ π§ 1 2 .

Q7:

Simplify 4 ( 9 0 + π 9 0 ) Γ 5 ( 8 0 + π 8 0 ) Γ 4 ( 4 5 + π 4 5 ) c o s s i n c o s s i n c o s s i n β β β β β β , giving your answer in trigonometric form.

Q8:

Given that and , find .

Q9:

What do we need to do to multiply two complex numbers in polar form?

Q10:

Given that and , where , determine the trigonometric form of .

Q11:

Given that , , , and , find .

Q12:

If π§ = 2 1 0 + π 2 1 0 1 β β c o s s i n , π§ = 3 ( 1 3 5 + π 1 3 5 ) 2 β β c o s s i n , and π§ = 4 ( 1 3 5 + π 1 3 5 ) 3 β β c o s s i n , what is the exponential form of ( π§ π§ π§ ) 1 2 3 4 ?

Q13:

Given that π§ = 2 ( 5 π + π 5 π ) ο§ c o s s i n and π§ = 4 ( 3 π β π 3 π ) ο¨ s i n c o s , determine π§ π§ ο§ ο¨ .

Q14:

If and , is it true that ?

Q15:

Given that , , and , where , find .

Q16:

Given that π§ = 3 οΌ 1 1 π 6 + π 1 1 π 6 ο c o s s i n , find 1 π§ in exponential form.

Q17:

Given that π§ = 2 ο» π 6 + π π 6 ο 1 c o s s i n and π§ = 1 β 3 ο» π 3 + π π 3 ο 2 c o s s i n , find π§ π§ 1 2 .

Q18:

Given that π§ = 5 ο» π 3 + π π 3 ο 1 c o s s i n and π§ = β 2 οΌ 5 π 6 + π 5 π 6 ο 2 c o s s i n , find π§ π§ 1 2 .

Q19:

Given that π§ = 5 οΌ 5 π 6 + π 5 π 6 ο ο§ c o s s i n and π§ = 4 ( 1 8 0 + π 1 8 0 ) ο¨ β β c o s s i n , determine π§ π§ ο§ ο¨ .

Q20:

Given that π§ = 2 ( ( 5 π β 2 π ) + π ( 5 π β 2 π ) ) 1 c o s s i n and π§ = 4 ( ( 4 π β 3 π ) + π ( 4 π β 3 π ) ) 2 c o s s i n , find π§ π§ 1 2 .

Q21:

Given that π§ = οΌ 7 π 6 ο + π οΌ 7 π 6 ο c o s s i n , find 1 π§ .

Q22:

Given that π§ = 2 β 3 ( 2 4 0 + π 2 4 0 ) c o s s i n β β , find π§ 2 in exponential form.

Q23:

Given that π§ = 4 ( 4 5 + π 4 5 ) 1 β β c o s s i n and π§ = 6 ( 9 0 + π 9 0 ) 2 β β c o s s i n , find the exponential form of π§ π§ 2 1 .

Q24:

Given that π§ = β 1 5 0 β π 1 5 0 1 β β s i n c o s and that π§ = 2 ( 1 2 0 β π 1 2 0 ) 2 β β s i n c o s , find π§ π§ 1 2 .

Q25:

Given that π§ = 1 2 β β 3 2 π 1 and π§ = 2 β 3 + 2 π 2 , find π§ π§ 1 2 , giving your answer in exponential form.

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