How do I divide 6(\cos^{\circ}60+i\sin60^{\circ}) by 3(\cos^{\circ}90+i\sin90^{\circ})?

Addison Gross

Addison Gross

Answered question

2022-01-31

How do I divide 6(cos60+isin60) by 3(cos90+isin90)?

Answer & Explanation

Jacob Trujillo

Jacob Trujillo

Beginner2022-02-01Added 13 answers

Step 1
The easiest way to divide complex numbers is to first convert to polar form and then you may divide modulus separately and subtract the angles.
Let z1=r1cisθ1=6cis60=6cos60+6isin60=660=6π3
z2=r2cisθ2=3cis90+3isin90=390=3π2
z1z2=r1r2cis(θ1θ2)
=63cis(6090)
=2cis(30)=230
=2(cos30isin30)
=3i

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