#Z= (3-5i)(7-8i) = (21-24i-35i+40i^2)#
# =21-59i-40 = -19-59i [i^2= -1]#
Modulus #|Z|=r=sqrt((-19)^2+ (-59)^2) =61.98 # ;
#tan alpha =b/a= (-59)/-19 = 3.105 :. alpha =tan^-1(3.105) = 1.259# or
#theta# is on #3rd# quadrant # :. theta=1.259+pi= 4.40 # rad
Argument : # theta =4.40 :. # In trigonometric form expressed as
#r(cos theta+isintheta) = 61.98(cos 4.40+isin4.40) :.#
# (3-5i)(7-8i) = 61.98(cos 4.40+isin4.40) # [Ans]