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   giorgiana1976 Teacher
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   Each complex number, whose algebric form is

   z=ai+b

   where a is the real part, a= Re(z) and b is the imaginary part, b=Im(z) and i is the imaginary unit, i^2=-1.

   The trigonometric form is:

   z=r(cos t + i sin t)

   r = (a^2 + b^2)^1/2

   r is the module of the complex number z.

   If a and b are the coordinates of a point M(a,b), r would be the radius vector of the point M.

   The formula for r = (a^2 + b^2)^1/2 results from Pythagorean theorem, where r is hypotenuse.

   cos t = a/r=>a=r cos t

   sin t = b/r=>b=r sin t

   z=a+bi=r cos t + ir sin t=r( cos t+i sin t)

    

    

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   Posted by giorgiana1976 on Saturday March 28, 2009 at 11:40 AM