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

1 Answer
Apr 25, 2017

2sqrt65 * ( cos theta + isin theta)265(cosθ+isinθ)

where, tan theta = 1/8 or theta = tan^-1(1/8)tanθ=18orθ=tan1(18)

Explanation:

(5-i)*(3+i)(5i)(3+i)

= 5*3+5i-3i-i*i=53+5i3iii

=15+2i-sqrt(-1)*sqrt(-1)=15+2i-(-1)=15+2i11=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+2i162+22162+22

=[16+2i]/[sqrt(260)]*sqrt(260)=16+2i260260

=2sqrt65[(16+2i)/(2sqrt65)]=265[16+2i265]

=2sqrt65[8/sqrt65+i/sqrt65]=265[865+i65]

=2sqrt65[8/sqrt65+i*1/sqrt65]=265[865+i165]

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=2sqrt65 * ( cos theta + isin theta)=265(cosθ+isinθ)

where, tan theta = 1/8 or theta = tan^-1(1/8)tanθ=18orθ=tan1(18)