Find the product of the complex numbers. Leave the answer

Joanna Benson

Joanna Benson

Answered question

2022-01-18

Find the product of the complex numbers. Leave the answer in polar form.
z1=6(cos40+isin40)
z2=5(cos20+isin20)

Answer & Explanation

Jordan Mitchell

Jordan Mitchell

Beginner2022-01-19Added 31 answers

Step 1
We know that
eiθ=cosθ+isinθ
Therefore,
z1=6(cos40+isin40)
=6ei(40)
z25(cos20+isin20)
=5ei(20)
Product of the complex numbers are:
z1z2=6ei(40)×5ei(20)
=30ei(40+20)
=30e60i
Therefore, product can be written as:
z1z2=30(cos60+isin60)

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