2 Find z1 and z2 and z1z2 express answers in polar form Plea

2.) Find z₁ and z₂ and z₁/z₂ express answers in polar form. Please show ALL your work.

a,) z₁ = cos/4+isin/4     z₂=cos3/4 + isin3/4

b.) z₁=4/5)cos25° +isin25°)   z₂=1/5(cos155° + isin155°)

Please show ALL your work.

Solution

2.) . first part cound not be understood so i am doing z1/z2:

a,) z1 = cos/4+isin/4    

in polar form z1 = 1e^(i*pi/4)

z2=cos3/4 + isin3/4

In polar form z2 = e^(i*3pi/4)

z1/z2 = e^(i3pi/4)/e^(ipi/4

= e^i(3pi/4-pi/4) = e^i*pi/2

In polar form z1/z2 = (1 , pi/2)

b.) z1=4/5(cos25° +isin25°)  

z1 = (4/5)e^i(25)

z2=1/5(cos155° + isin155°)

z2 = (1/5)e^i155

z1/z2 = 4e^i(155-25) = 4e^i(130)

In polar form z1/z2 = ( 4 , 130 deg)