# complex numbers notes pdf

We then write z = x +yi or a = a +bi. (Electrical engineers sometimes write jinstead of i, because they want to reserve i Complex numbers often are denoted by the letter z or by Greek letters like a (alpha). Also we assume i2 1 since The set of complex numbers contain 1 2 1. s the set of all real numbers… 7.3 Properties of Complex Number: (i) The two complex numbers a + bi and c + di are equal if and only if In coordinate form, Z = (a, b). Above we noted that we can think of the real numbers as a subset of the complex numbers. addition, multiplication, division etc., need to be defined. 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). 18.03 LECTURE NOTES, SPRING 2014 BJORN POONEN 7. This is termed the algebra of complex numbers. Complex Numbers. Complex numbers can be represented as points in the plane, using the cor-respondence x + iy ↔ (x, y). Having introduced a complex number, the ways in which they can be combined, i.e. Notes on Complex Numbers University of British Columbia, Vancouver Yue-Xian Li March 17, 2015 1. Table of contents. The representation is known as the Argand diagram or complex plane. Note that the formulas for addition and multiplication of complex numbers give the standard real number formulas as well. COMPLEX NUMBERS, EULER’S FORMULA 2. Complex Numbers notes.notebook October 18, 2018 Complex Conjugates Complex Conjugates­ two complex numbers of the form a + bi and a ­ bi. numbers and pure imaginary numbers are special cases of complex numbers. we multiply and divide the fraction with the complex conjugate of the denominator, so that the resulting fraction does not have in the denominator. Step Study handwritten notes... (0) Answer. Section 2.1 – Complex Numbers—Rectangular Form The standard form of a complex number is a + bi where a is the real part of the number and b is the imaginary part, and of course we define i 1. Dividing by a complex number: Multiply top and bottom of the fraction by the complex conjugate of the denominator so that it becomes real, then do as above. Dividing Complex Numbers Dividing complex numbers is similar to the rationalization process i.e. Dividing by a real number: divide the real part and divide the imaginary part. Examples: 3+4 2 = 3 2 +4 2 =1.5+2 4−5 3+2 = 4−5 3+2 ×3−2 3−2 The complex numbers are denoted by Z , i.e., Z = a + bi. Skip Notes. The real complex numbers lie on the x–axis, which is then called the real axis, while the imaginary numbers lie on the **The product of complex conjugates is always a real number. Deﬁnition (Imaginary unit, complex number, real and imaginary part, complex conjugate). But first equality of complex numbers must be defined. 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