Note that real numbers are complex a real number is simply a complex number with zero imaginary part. For example, 17 is a complex number with a real part equal to 17 and an imaginary part equalling zero, and iis a complex number with a real part of zero. The complex plane the real number line below exhibits a linear ordering of the real numbers. Imaginary and complex numbers worksheets kiddy math. Complex numbers complex numbers of the form iy, where y is a nonzero real number, are called imaginary numbers. See more on vectors in 2dimensions we have met a similar concept to polar form before, in polar coordinates, part of the analytical geometry section. A short history of complex numbers home department of.
The symbol i represents an imaginary number with the property i. It is important to note that any real number is also a complex number. Chalkboard photos, reading assignments, and exercises pdf 1. The plane in which one plot these complex numbers is called the complex plane, or argand plane. A strictly real or imaginary number is also complex, with the imaginary or real part equal to zero, respectively. For example, 5i is an imaginary number, and its square is. Introduction to complex numbers and complex solutions. In what follows i denotes the imaginary unit defined by i v 1. Students are required to identify the real part and the imaginary part. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2. Lesson plan mathematics high school math ii focusdriving. But there is no real number whose square is negative. Every real number is a complex number with 0 as its imaginary part.
Displaying all worksheets related to imaginary and complex numbers. Same numbers, different forms in an attempt to make life more difficult for the people learning about complex numbers, the people who had already mastered the argand diagram came up with a. The complex inverse trigonometric and hyperbolic functions. We can think of complex numbers as vectors, as in our earlier example. To emphasize this, recall that forces, positions, momenta, potentials, electric and magnetic. Traditionally the letters zand ware used to stand for complex numbers. Electrical engineers sometimes write jinstead of i, because they want to reserve i for current, but everybody else thinks thats weird. The unit imaginary number the equivalent of 1 for real numbers is v. There are a few rules associated with the manipulation of complex numbers which are worthwhile being thoroughly familiar with. Think of it as a marriage of the real and imaginary, a tasty cocktail of morpheuss proffered red and blue pills. In order to solve such equations it is necessary to expand the number system by defining an imaginary number i.
Because no real number satisfies this equation, i is called an imaginary number. The worksheet also provides practice in forming complex numbers with the given real part and the imaginary part. If two complex numbers are equal, we can equate their real and imaginary parts. Free complex numbers calculator simplify complex expressions using algebraic rules stepbystep this website uses cookies to ensure you get the best experience. A complex number is what we call the sum of a real number and an imaginary number. Complex numbers complex numbers pearson schools and fe. Graphically the absolute value of complex number is the distance from the origin to the complex point in the complex plane. Basic concepts of complex numbers operations on complex. In mathematics we use i for imaginary but in electronics they use j because i already means current, and the next letter after i is j. Students are more likely to learn with understanding if they have tried to extend their existing knowledge rather than be prescribed a rule.
The union of the set of all imaginary numbers and the set of all real numbers is the set of complex numbers. Next, lets take a look at a complex number that has a zero imaginary part. Algebra 2 curriculum this resource works well as independent practice, homework, extra credit or even as an assignment to leave for the s. If we add or subtract a real number and an imaginary number, the result is a complex number. To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator to.
Students will simplify 20 algebraic expressions with complex numbers imaginary numbers including adding, subtracting, multiplying and dividing complex numbers. Two complex numbers are said to be equal if they have the same real and imaginary parts. Its called the complex conjugate and all it is is a complex number with the sign of the imaginary part swapped, and is represented as a z with a bar over it. Use pythagorean theorem to determine the absolute value of this point.
Powers of complex numbers via polar forms 45 7 powers of complex numbers 46 7. Complex numbers form what is called a field in mathematics, which in a nutshell this is not a text in pure mathematics means that. Similarly, the imaginary numbers are also a subset of the complex numbers. Complex numbers beginning complex numbers math help. Having introduced a complex number, the ways in which they can be combined, i. Imaginary numbers are real free pdf download not printable 0. Imaginary numbers are real free pdf download welch labs. I n algebra, we want to be able to say that every polynomial equation has a solution. You can also determine the real and imaginary parts of complex numbers and compute other common values such as phase and angle. A complex number has two parts, a real part and an imaginary part. The complex numbers are listed in a tabular format. Despite the historical nomenclature imaginary, complex numbers are. Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts.
Combine the following complex numbers and their conjugates. The following notation is used for the real and imaginary parts of a complex number z. Plot the imaginary part versus the real part of a complex. Worksheets are operations with complex numbers, complex numbers and powers of i, dividing complex numbers, adding and subtracting complex numbers, real part and imaginary part 1 a complete the, complex numbers, complex numbers, properties of complex numbers. Real and imaginary parts the real and imaginary parts. Postscript or pdf produced by some word processors. Hence the set of real numbers, denoted r, is a subset of the set of complex numbers, denoted c. In other words, a real number is just a complex number with vanishing imaginary part.
Establish student understanding by asking students if they. Complex or imaginary numbers a complete course in algebra. So an imaginary number may be regarded as a complex number with a zero real part. To multiply complex numbers, distribute just as with polynomials. Imaginary and complex numbers displaying top 8 worksheets found for this concept some of the worksheets for this concept are operations with complex numbers, complex numbers and powers of i, dividing complex numbers, adding and subtracting complex numbers, real part and imaginary part 1 a complete the, complex numbers, complex numbers, properties of complex. In these cases, we call the complex number a pure imaginary number. The complex inverse trigonometric and hyperbolic functions in these notes, we examine the inverse trigonometric and hyperbolic functions, where the arguments of these functions can be complex numbers.