Show that arg z1 arg z2 arg z1z2 thus Express the following

Show that arg z_1 + arg z_2 arg z_1z_2, thus Express the following in a + ib form. E^1pi/2. 4e^-i pi/2. 8e^i7 pi/3. -2e^i 5 pi/6. 2ie^-I 3 pi/4. 6e^I 2 pi/3 e^i pi. E^2 e^i pi. e^I pi/4 - i pi.

Solution

Phasor form of complex number:

Z=|z| ( Cos + Sin) =|z| e

subset (b) = 4e ^-/2

Comparing this we get, |z|=4 and =-/2

so, It can be written in the form as follows:

z= 4 ( Cos(-/2) + i Sin(-/2) ) { Cos(-/2) = 0 ; Sin(-/2)= -1 }

z= 4 ( 0 - i ) = 0-4i ; a=0 , b=-4

subset (d) = -2 e ^i5/6

z= -2 ( Cos(5/6) + i Sin(5/6) ) { Cos(5/6) = -3/2 ; Sin(5/6)=1/2 }

z= -2 ( -3/2 + i 1/2 )

z= 3 + i ; a=3 , b=1