So a number is imaginary if its second power is a

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Unformatted text preview: sible: 1). If a = 0 , then x = 0. 2). If a is a positive number, then its square root has two values: one positive and one negative; for example, the equation x2 = 25 has the two roots: 5 and –5. This is often written as the root with double sign before: 3). If a – a negative number, then the equation has no solution among known us positive and negative numbers, because the second power of any number is a non-negative number (think over this!). But, if we wish to receive solutions of the equation x2 = a also at negative values of a, we are obliged to introduce the new kind numbers – imaginary numbers. So, a number is imaginary, if its second power is a negative number. According to this definition of imaginary numbers we can define an imaginary unit as: Then, for the equation x2 = – 25 we receive the two imaginary roots: roots into our equation we’ll receive the identity. Check it, please! Substituting both these In contrast to imaginary numbers all the rest numbers (positive and negative, integers and fractional, rational and irrational ones) are called real numbers. A sum of a real and an imaginary number is called a complex number, and marked as: a+bi , Math I - 19 - Feel free to pass this on to your friends, but please don’t post it online. Discuss UPCAT and other college entrance exam questions and answers at Academic-Clinic’s Facebook Page. We encourage you to answer the questions we post there and actively participate in the discussions on our wall. For UPCAT, ACET, DLSUCET and USTET tips, tricks, news and other college entrance exam information, visit the Academic-Clinic website. Tell your friends and classmates to come find and join us. The more, the merrier. Good luck! AcademicAcademic Academic-Clinic.com The achiever’s guide to academic life and beyond… W ebsite: http://academic-clinic.com Facebook: http://www.facebook.com/academic.clinic Twitter: http://twitter.com/acadclinic College entrance exam and science high school entrance test tips. Conquer UPCAT, ACET, USTET, DL...
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This note was uploaded on 07/21/2013 for the course UPCAT 2014 taught by Professor Otis during the Spring '13 term at University of the Philippines Diliman.

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