Rewrite the above complex number in the usual form z=x+iy as follows.
[multiply and divide by the conjugate 1−i of 1+i]
Compare the complex number with z=x+iy and obtain and
The argument of a complex number z=x+iy is given by
Since both and are positive, the complex number lie in the 1st quadrant.
Hence, its principal argument is the same as
The exponential form of a complex number z=x+iy with principal argument theta is given by where
For the value
Hence, the exponential form of is is
Thus, the principal argument of is and the exponential form is