Intro to Complex Numbers.pptx
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This document introduces complex numbers. It explains that complex numbers are written in the form a + bi, where a is the real part and b is the imaginary part. It provides rules for adding, subtracting, multiplying, and dividing complex numbers. It also gives examples of performing each operation on complex numbers. Finally, it introduces that powers of i follow a repeating pattern where i squared is equal to -1.
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Complex Numbers
The document discusses complex numbers. It begins by defining pure imaginary numbers as any positive real number b multiplied by the imaginary unit i, where i^2 = -1. It then defines i as the square root of -1. The document proceeds to simplify various expressions involving complex numbers. It introduces the concept of a cycle of i where the value repeats every 4 exponents. It defines complex numbers as numbers in the form a + bi, where a and b are real numbers. The document concludes by showing how to add, subtract, and multiply complex numbers by distributing like terms.
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Imaginary numbers are square roots of negative real numbers that were introduced to allow taking the square root of negatives. An example of an imaginary number is 2i√6, where i represents the imaginary unit. Imaginary numbers can be added, subtracted, multiplied, and divided like real numbers. When squared, imaginary numbers follow a repeating sequence of i, -1, -i, 1. Though sometimes complex, imaginary numbers serve an important purpose and are generally easy to work with through practice and logical thinking.
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The document provides an introduction to complex numbers including:
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- Properties of i including i2 = -1.
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- Operations on complex numbers such as addition, subtraction, multiplication and division.
- Comparing real and imaginary parts of complex numbers when solving equations.
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The document introduces complex numbers and their properties. It defines the imaginary unit i as the square root of -1. Complex numbers have both a real and imaginary part and can be added, subtracted, multiplied and divided. Powers of i rotate through the values of i, -1, -i, and 1, depending on whether the exponent is 1, 2, 3, or 4 modulo 4. Real and imaginary numbers are subsets of complex numbers.
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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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- 1. Introduction to Complex Numbers Adding, Subtracting, Multiplying And Dividing Complex Numbers SPI 3103.2.1 Describe any number in the complex number system.
- 2. Complex Numbers (a + bi) Natural (Counting) Numbers Imaginary #’s
- 3. Complex Numbers are written in the form a + bi, where a is the real part and b is the imaginary part. a + bi real part imaginary part
- 4. When adding complex numbers, add the real parts together and add the imaginary parts together. (3 + 7i) + (8 + 11i) real part imaginary part 11 + 18i
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- 8. 7 + 2i 3 – 5i 21 + 35i + 6i + 10i2 9 + 15i – 15i – 25i2 21 + 41i – 10 9 + 25 (3 + 5i) (3 + 5i) 11 + 41i 34
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