Find the quotient z1z2 of the complex numbers z1=10(cos⁡10∘+isin⁡10∘) and z2=5(cos⁡5∘+isin⁡5∘) Leave answers in polar...

percibaa8

percibaa8

Answered

2022-01-18

Find the quotient z1z2 of the complex numbers
z1=10(cos10+isin10)
and z2=5(cos5+isin5)
Leave answers in polar form.

Answer & Explanation

lovagwb

lovagwb

Expert

2022-01-19Added 50 answers

Step 1
z1z2=10(cos10+isin10)5(cos5+isin5)
z1z2=2(cos10+isin10)(cos5+isin5)
z1z2=2[(cos10+isin10)(cos5+isin5)×(cos5isin5)(cos5isin5)]
z1z2=2[cos10cos5isin5cos10+isin10cos5isin10isin5(cos5+isin5)(cos5isin5)]
z1z2=2[cos10cos5+isin5cos10isin10cos5+isin10isin5(cos5+isin5)(cos5isin5)]

Lynne Trussell

Lynne Trussell

Expert

2022-01-20Added 32 answers

Step 1
The quotient z1z2 of the complex number, and leave the answer in Polar form.
Given: The complex numbers are z1=10(cos10+isin10) and z2=5(cos5+isin5)
Concept used:
(cosθ+isinθ)=eiθ
Step 2
Calculation:
The quotient z1z2 can be obtained as,
z1z2=10(cos10+isin10)5(cos5+isin5)
=2e10ie5i
=2e(10i5i)
=2(cos5+isin5)
Thus, the quotient z1z2 of the complex numbers is z1z2=2(cos5+isin5)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?