MATH 475 Study Guide - Final Guide: Polar Coordinate System, Modulus Guitars, Taylor Series
9 Jun 2020
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Maxwell lovig (z) = x and im(z) = y. |z| = px2 + y2 (modulus) z1 + z2 = (re(z1) + re(z2)) + (im(z1) + im(z2))i (z1)(z2) = re(z1)re(z2) (im(z1)re(z2) + re(z1)im(z2))i im(z1)im(z2) (using foil) z1 z2 z1z2. In fact any cartesian complex number can be expressed in polar coordinates: rei , r = |z|, = arctan ( y x. A less useful form isz = |z|(cos ( ) + i sin ( )) Shapes in the complex plain represent sets of complex numbers, the most common of which is a circle. Described by |z z0| = or < or > r (represents |z| = 1 and |z| < 1) Polynomials, to solve a polynomial in complex coordinates there a multiple techniques: The fundamental theorem of algebra tells us that for a n-degree polynomial there are n complex roots, counting multiplicity. For a an equation zn = z+, such as z4 = 1, we have each root of unity.
