![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: ![]() If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the We start by defining the imaginary unit i i as the number whose square is –1. All of these together gave us the real numbers and so far in your study of mathematics, that has been sufficient.īut now we will expand the real numbers to include the square roots of negative numbers. Adding the irrational numbers allowed numbers like 5. ![]() When they needed the idea of parts of a whole they added fractions and got the rational numbers. When they needed negative balances, they added negative numbers to get the integers. They added 0 to the counting numbers to get the whole numbers. Mathematicians have often expanded their numbers systems as needed. Since all real numbers squared are positive numbers, there is no real number that equals –1 when squared. For example, to simplify −1, −1, we are looking for a real number x so that x 2 = –1. z is a Complex Number a and b are Real Numbers i is the unit imaginary number 1 we refer to the real part and imaginary part using Re and Im like this: Re(z. We often use the letter z for a complex number: z a + bi. A complex number is expressed in standard form when written a + bi where a is the real part and bi is the imaginary part. A complex number can now be shown as a point: The complex number 3 + 4i. Whenever we have a situation where we have a square root of a negative number we say there is no real number that equals that square root. A complex number is the sum of a real number and an imaginary number. Evaluate the Square Root of a Negative Number If you missed this problem, review Example 5.32.
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