1.

Convert of the complex number in the polar form: `1-i`

Answer» Polar form of a complex number is given by,
`r(costheta+isintheta)`
So, `1-i = r(costheta+isintheta)`
Comparing, real and unreal part,
`rcostheta = 1 and rsintheta = -1`
Squaring and adding both expression,
`r^2cos^2theta + r^2sin^2theta = 1+1`
`r^2(cos^2theta+sin^2theta) = 2`
`r = sqrt(2)`
So, `sintheta = -1/sqrt2 and costheta = 1/sqrt2`
So, polar form will be `sqrt2(1/sqrt2-1/sqrt2i)`


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