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Magnitude and Phase of Complex Numbers
gubner.ece.wisc.eduFigure 2. A complex number z=x+ jy in the second quadrant of the complex plane. q >p=2, we apply the theory of right triangles to the the supplementary angle p q. Since x is negative, the length of the horizontal side is x. Thus, tan(p q) = y=( x), and, since tan 1 is an odd function, it follows that q =p+tan 1(y=x). Since
Section 6.5, Trigonometric Form of a Complex Number
www.math.utah.eduThe absolute value of a complex number is its distance from the origin. If z= a+ bi, then jzj= ja+ bij= p a2 + b2 Example Find j 1 + 4ij. j 1 + 4ij= p 1 + 16 = p 17 2 Trigonometric Form of a Complex Number The trigonometric form of a complex number z= a+ biis z= r(cos + isin ); where r= ja+ bijis the modulus of z, and tan = b a. is called the ...