(5-i)*(3+i)(5−i)⋅(3+i)
= 5*3+5i-3i-i*i=5⋅3+5i−3i−i⋅i
=15+2i-sqrt(-1)*sqrt(-1)=15+2i-(-1)=15+2i−√−1⋅√−1=15+2i−(−1)
=15+2i+1=15+2i+1
=16+2i=16+2i
=(16+2i)/(sqrt(16^2+2^2))*sqrt(16^2+2^2)=16+2i√162+22⋅√162+22
=[16+2i]/[sqrt(260)]*sqrt(260)=16+2i√260⋅√260
=2sqrt65[(16+2i)/(2sqrt65)]=2√65[16+2i2√65]
=2sqrt65[8/sqrt65+i/sqrt65]=2√65[8√65+i√65]
=2sqrt65[8/sqrt65+i*1/sqrt65]=2√65[8√65+i⋅1√65]
=2sqrt65 * ( cos theta + isin theta)=2√65⋅(cosθ+isinθ)
where, tan theta = 1/8 or theta = tan^-1(1/8)tanθ=18orθ=tan−1(18)