1.

1-i

Answer»


Solution :LET `1-i=r(costheta+isintheta)`
then `rcostheta=1 andr sintheta=-1`
SQUARING and adding both equations,
`r^(2)COS^(2)theta+ r^(2)sin^(2)theta=(1)^(2)+(-1)^(2)=1+1=2`
`rArr""r^(2)(cos^(2)+sin^(2)theta)=2" "rArr" "r^(2) =2 orr=sqrt(2)`
and `""TANTHETA=(rsintheta)/(rcos theta )=(-1)/(1)=-1`
`""=TAN(-45^(@))=tan(-(pi)/(4))`
`rArr""theta=(-pi)/(4)`
Therefore, `1-i=r(costheta+isintheta)`
`""=sqrt(2)[ cos(-(pi)/(4))+sin((-pi)/(4))]`


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