Science and nature Math Girl's Secret Note / Complex Number Spread

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Science and Nature In Chapter 1, "The Spread of Squares," we begin with a simple question, "What happens when you square a number?", and then examine the properties of numbers. By comparing numbers and multiplying positive and negative numbers, we become familiar with the basic properties of numbers. We also study simple quadratic equations and quadratic functions through graphs. In chapter 2, "Forms of Calculation," we study complex numbers while drawing points on a plane. By examining the similarities and differences between real and imaginary numbers, we understand complex numbers. Instead of mechanically learning the rules of calculation, we study the relationships between complex numbers and polar forms and between complex numbers and trigonometric functions. In chapter 3, "The Shadow of a Star on the Surface of Water," we study conjugate complex numbers. Using concrete figures called regular pentagons, we capture the meaning and role of conjugate complex numbers and experience the relationship between calculations and figures. In chapter 4, "The Building Pentagon," we draw regular pentagons with rulers and compasses. Instead of simply drawing figures, we look at the manipulation of numbers and their algebraic meaning one by one. By doing so, we study the interrelationships of many mathematical concepts such as equations, trigonometric functions, Do Moab's formula, the n-th power of 1, and matrices. In chapter 5, "Finding the Spread," we try to expand the "two dimensional number" of complex numbers. Through trial and error to create "three dimensional number" and "four dimensional number," we re-examine the rules of numbers such as commutative law, associative law, and distribution laws. In addition, we use matrices to express numbers and construct quaternions, and we close this book.