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July 2004. Abstract. This article discusses some introductory ideas associated with complex numbers, their algebra and geometry. This includes a look at their importance in solving polynomial equations, how complex numbers add and multiply, and how they can be represented.
complex numbers – find the reduced row–echelon form of an matrix whose el- ements are complex numbers, solve systems of linear equations, find inverses and calculate determinants.
complex. Addition and subtraction of complex numbers has the same geometric interpretation as for vectors. The same holds for scalar multiplication of a complex number by a real number. (The geometric interpretation of multiplication by a complex number is di erent; we'll explain it soon.)
Any complex number is then an expression of the form a + bi, where a and b are old-fashioned real numbers. The number a is called the real part of a + bi, and b is called its imaginary part. Traditionally the letters z and w are used to stand for complex numbers.
a real number, f(x) is a complex number, which can be decomposed into its real and imaginary parts: f ( x ) = u ( x )+ iv ( x ), where u and v are real-valued functions of a real variable; that is, the objects you are familiar with from
If a = a + bi is a complex number, then a is called its real part, notation a = Re( a ), and b is called its imaginary part, notation b = Im( a ). The imaginary part,
Complex Numbers † Complex numbers have both real and imaginary components. A complex number r may be expressed in Cartesian or Polar forms: r = a+jb (cartesian) = jrje` (polar) The following relationships convert from cartesian to polar forms: Magnitude jrj = p a2 +b2 Angle ` = (tan¡1 b a a > 0 tan¡1 b a §… a < 0 † Complex numbers can ...
