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Find the modulus, argument, and the prin...

Find the modulus, argument, and the principal argument of the complex numbers. (i) `(tan1-i)^2`

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`z = (tan1 - i)^(2) = (tan^(2) 1-1)- (2 tan1)i`
`|z|= sqrt((tan^(2)1-1)^(2) + 4 tan^(2)1)=sqrt((tan^(2)1+1)^(2))= sec^(2)1`
Since `tan^(2) 1- 1 lt 0 and -2 tan 1 lt 0,` so z lies in the third quadrant.
`rArr " " arg(z) = - pi + tan^(-1)|(2 tan1)/(1-tan^(2))| = - pi + tan^(-1)|tan2| = 2pi`
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