Abstract A complex number is a number that can be written in the form of a+bi where a and b are real numbers and i is the value of the square root of negative one. In the form a + bi‚ a is considered the real part and the bi is considered the imaginary part. The goal of this project is show how the use of complex numbers originates in the history of mathematics. Introduction Complex numbers are very important component of mathematics. They enable us to solve any polynomial equation of degree
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Pythagoras Birthdate: 569 B.C. Died: 475 B.C. Nationality: Greek Contributions: * Pythagorean Theorem. In a right angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides. Note: A right triangle is a triangle that contains one right (90°) angle. The longest side of a right triangle‚ called the hypotenuse‚ is the side opposite the right angle. The Pythagorean Theorem is important in mathematics‚ physics‚ and astronomy and has practical applications
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MODULE 1: Quadratic Equation Lesson No. of Hours Learning Competency Activity Lesson 1: Illustrations of Quadratic Equations 1 Illustrate quadratic equations Activity 1 Lesson 2.1: Solving Quadratic Equations by Extracting Square Roots 1 Solve quadratic equations by extracting square roots Activity 2 Lesson 2.2: Solving Quadratic Equations by Factoring 1 Solve quadratic equations by factoring Lesson 2.3: Solving Quadratic Equations by Completing the Square 1 Solve quadratic equations
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During their period of time‚ the pythagoreans were a political factor in Syracuse. The pythagoreans would dress simply and eat very little. They followed a strict regime. They had to be silent and obedient‚ and could not adorn their body with jewelry‚ and practiced a lot of self-examination. The pythagoreans viewed true friendship as very important. Damon and Pythias were the ideal Pythagorean friendship for their time. The love and power of friendship can move
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Algebra 222 week 4 Quiz CLOSE WINDOW Week 4: Quadratic Equations and Functions‚ Date Submitted: 10/26/2014 1. Finding the roots of a quadratic equation with leading coefficient 1 Solve for y . =+y2−3y40 If there is more than one solution‚ separate them with commas. If there is no solution‚ click on "No solution." You answered correctly: =y− 4‚1 2. Finding the roots of a quadratic equation with leading coefficient greater than 1 Solve for v . =2v2+3v2 If there is more than one solution
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Pythagoras is commonly known for his discovery of the “Pythagorean Theorem”. The Pythagorean thereom states that the‚ “Square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides: c2 = a2 + b2” (Pyhtagorean…). Without Pythagoreas or his invention we would not
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whether each statement is always‚ sometimes‚ or never true. 1. The graph of a quadratic function is a straight line. 2. The range of a quadratic function is the set of all real numbers. 3. The highest power in a quadratic function is 2. 4. The graph of a quadratic function contains the point (0‚ 0). 5. The vertex of a parabola occurs at the minimum value of the function. 6. The graph of a quadratic function that has a minimum opens upward. 7. The graphs of f(x) = ax2 and gx=
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The Parabola What is a Parabola? A quadratic expression is an expression in which the highest power of is 2. Consider the following: The above equations are all quadratic expressions as the highest power of is 2. When a quadratic function is graphed‚ the resulting curve is called a parabola‚ as demonstrated in figures 1 and 2. Real Life Application A quadratic function and parabola can be used when undertaking a new business venture to determine the optimum sales price of a particular
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other areas Hippasus Hippasus is credited with the discovery of irrational numbers. The Pythagoreans were a strict society and all discoveries that happened had to be directly credited to them‚ not the individual responsible for the discovery. The Pythagoreans were very secretive and did not want their discoveries to get out. They all took oaths to ensure that their discoveries remained with the Pythagorean society. They considered whole numbers to be their rulers and that all quantities could be
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The Ancient Greeks contributed a lot to modern society‚ but the biggest contribution of them was their contributions to the field of science and mathematics. To start off‚ the Pythagorean theorem contributed a lot to the field of mathematics. What the Pythagorean theorem does is help us to calculate the lengths of the sides of right triangles. Secondly‚ Archimedes contributed a ton to both fields. One of the most famous things that Archimedes did was find out if a crown that the king had ordered
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