Find the quotient \frac{z_{1}}{z_{2}} of the complex numbers.Leave answers in

kerrum75

kerrum75

Answered question

2022-01-18

Find the quotient z1z2 of the complex numbers.Leave answers in polar form.Express the argument as an angle between 0 and 360.
z1=cos70+isin70
z2=cos230+isin230

Answer & Explanation

Philip Williams

Philip Williams

Beginner2022-01-19Added 39 answers

Step 1
As we know that:
cosθ+isinθ=eiθ
Therefore,
z1=cos70+isin70
=ei(70)
Step 2
And
z2=cos230+isin230
ei(230)
Therefore,
z1z2=ei(70)ei(230)
=ei(70)×ei(230)
=ei(70230)
=ei(160)
=e160}×1
=e160}×ei(360) (because ei(360)=1)
=ei(160+360)
=ei(200)
=cos(200)+isin(200)
Step 3
Therefore the quotient z1z2 of the complex numbers in polar form having argument as an angle between 0 and 360 is cos(200)+isin(200)

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