Understand and use complex numbers, including real and imaginary numbers, on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number.
I Can Statements
*I can identify complex numbers.
*I can identify the real and imaginary parts of a complex number.
*I can graph complex numbers on the complex plane in rectangular form.
*I can graph complex numbers on the complex plane in polar form.
*I can translate between rectangular and polar forms of a complex number.
*I can justify why the rectangular and polar forms of a complex number represent the same number.
* Know that there is an imaginary number, i, such that √− 1 = i. Understand that the imaginary numbers along with the real numbers form the complex number system. (MA.AI.NE.1)
*Use the discriminant to determine the number and type of solutions of a quadratic equation; write complex solutions in the form of a ± bi for real numbers a and b. (MA.AII.Q.4)
*Areas bounded by polar curves can be calculated with definite integrals. (CB.EK3.4D1 BC)
*For a curve given by a polar equation r =f(theta), derivatives of r, x, and y with respect to theta and first and second derivatives of y with respect to x can provide information about the curve. (CB.EK2.2A4 BC)
Clarifying Examples and Digital Resources
Click here for clarifying examples and digital resources aligned to Indiana standards. These are intended to expand each standard to support instruction in the classroom as evidenced by the Eight Mathematics Teaching Practices put forth by the National Council of Teachers of Mathematics (NCTM).