Rational Exponents and Complex Numbers

How do weather forecasters create models to determine if an umbrella is needed that day? Rational exponents play an important mathematical role by connecting powers and roots, as well as in real-world financial situations like depreciation and inflation. Complex numbers ensure that every algebraic equation has a solution, and they make the work of designing Wi-Fi equipment, electric cars, and wind turbines easier. In M202 Rational Exponents and Complex Numbers, you will complete your study of the real number system and extend your study of numbers beyond it to the complex number system. As you make sense of rational exponents and complex numbers, you will evaluate and simplify numerical and algebraic expressions involving radicals and rational exponents, solve simple rational and radical equations in one variable, and add, subtract, and multiply complex numbers. Additionally, you will solve quadratic equations with real coefficients containing non-real solutions and that represent complex numbers on the complex plane in rectangular form. Complex numbers are beneficial in describing many real-world situations, such as the laws of electricity and electromagnetism. Both rational exponents and radical expressions are useful for careers in a variety of fields, like architecture, carpentry, electrical engineering, finance, and masonry.

Suggested prerequisites for this badge: M103 Modeling with Functions of Quadratic Type; M104 Modeling with Functions of Exponential Type.