What is the trigonometric form of # (5-2i)(2+3i) #?

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Answer 1 · 2016-01-06T09:46:11

#sqrt(377){cos(tan^-1(11/16))+isin(tan^-1(11/16))}#

#(5-2i)(2+3i)#

Multiply using FOIL

#(5)(2)+5(3i)+(-2i)(2)+(-2i)(3i)#
#10+15i-4i-6i^2#
#=10+11i-6(-1)# since #i^2=-1#
#=10+6+11i#
#=16+11i#

Trigonometric form is #r(cos(theta)+isin(theta))#
if #z=x+iy#

#r=sqrt(x^2+y^2)# and #theta = tan^-1(y/x)#

#r=sqrt(16^2+11^2)# and #theta = tan^-1(11/16)#
#r=sqrt(256+121)#
#r=sqrt(377)#
Trigonometric form

#sqrt(377){cos(tan^-1(11/16))+isin(tan^-1(11/16))}#