complex into polar form

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May 8th, 2015

(a) The angle theta of the polar representation is given by:

Tan (theta)= (imaginary  part)/real part) = -1/1 = 1 => theta = 135 deg = 3pi/4

radius of polar form = sqrt(real^2+ imaginary^2) = sqrt(1+1)=sqrt(2)

the polar form is sqrt(2)(cos(3pi/4) + isin(3pi/4)

(b) - OK

(c) The radius (length of line connecting the origin to the point (1,i) is sqrt (1+1)=sqrt(2)

The angle of that line with respect to the x-axis - theta= 45 deg (by simple geometry - it is the side angle of an isosceles right angle triangle so it must be 45 degrees)

z=sqrt(2)(sin (pi/4) + i cos(pi/4))


pls. best


May 8th, 2015

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