Find the product of the complex numbers z_{1}=6(cos20^{\circ}+i \sin 20^{\circ}) and

veksetz

veksetz

Answered question

2021-12-18

Find the product of the complex numbers
z1=6(cos20+isin20) and z2=5(cos50+isin50). Leave answers in polar form.

Answer & Explanation

Jillian Edgerton

Jillian Edgerton

Beginner2021-12-19Added 34 answers

Step 1
the given complex numbers are:
z1=6(cos20+isin20)
z2=5(cos50+isin50)
Step 2
as we know that eiθ=cosθ+isinθ
therefore,
z1=6e20i
and z2=5e50i
therefore, the product of the two complex numbers is:
z1z2=(6e20i)(5e50i)
=30e20i+50i
=30e70i
=30(cos70+isin70)
therefore the product of the two complex numbers in polar form is 30(cos70+isin70)
Linda Birchfield

Linda Birchfield

Beginner2021-12-20Added 39 answers

Step 1
z1×z2=6×5(cos(20+50)+i×sin(20+50))
z1×z2=30×(cos(70)+i×sin(70))
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

Step 1
Given:
z1=6(cos20+isin20); z2=5(cos50+isin50)
By using concept z1, z2 are rewritten as
z1=6cos20; z2=5cos50
z1z2=6×5cos(20+50) (By using concept)
=30cos(70)
=30(cos(70)+isin70) (In the form a+ib)
Answer: z1z2=30cos70+i30sin70
or z1z2=30(cos70+isin70) (In polar form)

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