Complex Numbers

This math unit begins with a deep dive into the fundamentals and properties of complex numbers, starting with rewriting roots involving negative radicands into complex number expressions and simplifying such forms. As students progress, they engage in operations of complex numbers including subtraction, division (focusing on imaginary parts), and the evaluation of powers of the imaginary unit \(i\). A gradual transition into geometric representations occurs as students practice calculating the absolute value of complex numbers on the complex plane. Further advancement in the unit includes converting complex numbers between different forms; initially from polar (in radians) to rectangular form, and from rectangular back to polar form in degrees. The unit also involves converting complex numbers from exponential form expressed in radians to rectangular form, utilizing Euler's formula. Towards the unit's end, a shift to pure geometry is observed where students apply the Pythagorean Theorem to calculate the length of a hypotenuse in decimal form, thereby bridging complex number theory with practical geometry applications. This progression allows students to not only understand but also manipulate complex numbers in various mathematical contexts and representations.Skills you will learn include:

• Meaning of i
• Complex plane
• Polar coordinates