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

1 Answer
Apr 25, 2017

2sqrt65 * ( cos theta + isin theta)

where, tan theta = 1/8 or theta = tan^-1(1/8)

Explanation:

(5-i)*(3+i)

= 5*3+5i-3i-i*i

=15+2i-sqrt(-1)*sqrt(-1)=15+2i-(-1)

=15+2i+1

=16+2i

=(16+2i)/(sqrt(16^2+2^2))*sqrt(16^2+2^2)

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

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

=2sqrt65[8/sqrt65+i/sqrt65]

=2sqrt65[8/sqrt65+i*1/sqrt65]

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=2sqrt65 * ( cos theta + isin theta)

where, tan theta = 1/8 or theta = tan^-1(1/8)