#" "#
Multiply the two complex numbers #(9-4i)*(2-i)# using #FOIL# Method.
#(9-4i)*(2-i)#
#rArr18-9i-8i+4i^2#
#rArr 18-17i+4*(-1)#
Note: #i^2=(-1)#
#rArr 18-17i-4#
#rArr14-17i#
Hence, #color(red)((9-4i)*(2-i)=14-17i# Intermediate Result 1
Convert this intermediate result to Trigonometric Form.
For a complex number in standard form: #color(blue)(z=a+bi#,
#r=sqrt(a^2+b^2#
#theta =tan^(-1)(b/a)#
#cos (theta) = a/r#
#rArr a=r*cos(theta)#
#sin(theta)=b/r#
#rArr b=r*sin(theta)#
#:. z=r*[cos(theta)+i*sin(theta)]#
Using Intermediate Result 1,
#r=sqrt(a^2+b^2#
#rArr sqrt(14^2+(-17)^2#
#rArr sqrt(196+289#
#rArr sqrt(485#
#:. r ~~ 22.02272#
#theta = tan^(-1)(b/a)#
#rArr tan^(-1)((-17)/14)#
#theta=tan^(-1)(-1.21429)#
#theta ~~-50.52763939^@#
#theta ~~ -50.5^@#
Hence,
#color(red)(z=22.0*[cos(-50.5^@)+i*sin(-50.5^@)]#
Hope it helps.
