Find zw and \frac{z}{w}. Write each answer in polar form

Tajzler6ek

Tajzler6ek

Answered question

2022-03-02

Find zw and zw. Write each answer in polar form and in exponential form.
z=7(cosπ4+isinπ4)
w=7(cosπ10+isinπ10)
The product zw in polar form is ? and in exponential form is ?.

Answer & Explanation

tardanetkd2

tardanetkd2

Beginner2022-03-03Added 9 answers


zw=r1r2[cos(θ1+θ2)+isin(θ1+θ2)]
Complex number product in polar form should be used.
zw=r1r2[cos(θ1θ2)+isin(θ1θ2) 
in exponential form
z=aeiθ
w=beiϕ
zw=77[cos(π4+π10)+isin(π4+π10)]
zw=49[cosπ2+isinπ2]
zw=49[cos7π20+isin7π20]
Similarly we will solve for zw
zw=cos3π20+isin3π20
now we will find exponential form which will be
zw=49ei(7π20)

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