Find zw andzw. Leave your answers

Answered question

2022-05-09

Find zw and

zw. Leave your answers in polar form.

 

 

z=10(cos150+i sin150)

w=6(cos200+i sin 200)

what is the product?

what is the quotient

 

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-06Added 106 answers

We are given two complex numbers in polar form:
z=10(cos150+isin150)
w=6(cos200+isin200)
To find the product zw, we can multiply the magnitudes and add the angles:
zw=|z||w|(cos(θz+θw)+isin(θz+θw))
where |z|=10, |w|=6, θz=150, and θw=200.
|z||w|=10·6=60, and θz+θw=150+200=350. However, since 350 is greater than 360, we need to subtract 360 to get the angle in the range of 0 to 360. Thus,
θz+θw=350360=10
Therefore, the product zw is:
zw=60(cos(10)+isin(10))
Using the identity cos(θ)=cosθ and sin(θ)=sinθ, we can simplify the expression to:
zw=60(cos10isin10)
Thus, the product zw is 60 in magnitude and has an angle of 10 in polar form.

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