How do you multiply # (1+7i)(-3+2i) # in trigonometric form?

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Answer 1 · 2017-11-19T11:05:42

# (1+7i)(-3+2i) ~~ 25.495 (cos 228.18+isin228.18)#

#Z= (1+7i)(-3+2i) = (-3+2i-21i+14i^2)#

# =-3-19i-14 = -17-19i [i^2= -1]#

#Z# lies on #3rd# quadrant

Modulus #|Z|=r=sqrt((-17)^2+ (-19)^2) ~~25.495 # ;

#tan alpha =b/a= (-19)/-17 ~~ 1.1176 :. alpha =tan^-1(1.1176) ~~ 48.18^0#

Since #Z# is on #3rd# quadrant # :. theta=pi+alpha# or

#theta= 180+48.18= 228.18^0 #. Argument : # theta =228.18^0 #

In trigonometric form expressed as #r(cos theta+isintheta)#

# = 25.495 (cos 228.18+isin228.18) #

# :. (1+7i)(-3+2i) ~~ 25.495 (cos 228.18+isin228.18)# [Ans]