Find the product \(\displaystyle{z}_{{{1}}}{z}_{{{2}}}\) and the quotient

Willie Kelley

Willie Kelley

Answered question

2022-04-06

Find the product z1z2 and the quotient z1z2. Express your answers in polar form.
z1=78(cos(35)+isin(35)),z2=18(cos(135)+isin(135))
z1z2=?
z1z2=?

Answer & Explanation

Videoad3u

Videoad3u

Beginner2022-04-07Added 15 answers

Step 1
For multiplication of complex numbers the angles add.
z1z2
=(78(cos(35)+isin(35)))×(18(cos(135)+isin(135)))
=(78×18)×(cos(35)+isin(35))×(cos(135)+isin(135))
764(cos(35+135)+isin(35+135))
=764(cos(170)+isin(170))
Step 2
For the division of complex numbers the angles subtract.
z1z2
=(78(cos(35)+isin(35)))(18(cos(135)+isin(135)))
=7(cos(35135)+isin(35135))
=7(cos(100)+isin(100))
=7(cos(100)isin(100))
Answer: z1z2=764(cos(170)+isin(170))
z1z2=7(cos(100)isin(100))

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