# (3+i)/(9-i)# #Z=a+ib #. Modulus: #|Z|=sqrt (a^2+b^2)#;
Argument: #theta=tan^-1(b/a)# Trigonometrical form :
#Z =|Z|(costheta+isintheta);Z_1= 3+ i #.
Modulus:#|Z_1|=sqrt(3^2+1^2)~~ 3.16 #
Argument: #tan alpha= (|1|)/(|3|):. alpha = tan^-1(1/3)~~0.32#
#Z_1# lies on first quadrant, so #theta =alpha ~~ 0.32#
# :. Z_1=3.16(cos 0.32+isin 0.32) #
#Z_2= 9 - i #. Modulus:#|Z_2|=sqrt(9^2+1^2) #
#=sqrt 82~~ 9.06# Argument: #tan alpha= (|-1|)/(|9|)#
#=1/9 :.alpha =tan^-1 (1/9) = 0.11 ; Z_2# lies on fourth
quadrant.#:. theta=2pi-alpha ~~6.17#
# :. Z_2=9.06(cos 6.17+isin 6.17) :. (3+i)/(9-i) =#
# Z= (3.16(cos0.32+isin 0.32))/(9.06(cos 6.17+isin6.17)#
#Z=0.35(cos(0.32-6.17)+isin (0.32-6.17))# or
#Z=0.35(cos 5.85 +i sin 5.85) =13/41+6/41 i#
In trigonometric form; #0.35(cos 5.85 +i sin 5.85)#
