MA19.PRE.4 | ALEX

Mathematics (2019) Grade(s): 09-12 - Precalculus

Students know:

Complex numbers are represented geometrically in the complex plane with the real part measured on the x-axis and the imaginary is represented on the y-axis.
Complex numbers can be added or subtracted by combining the real parts and the imaginary parts or by using vector procedures geometrically (end-to-end, parallelogram rule).
The product of complex numbers in polar form may be found by multiplying the magnitudes and adding the arguments.

Students are able to:

Add, subtract, and multiply the component parts of complex numbers to find sums, differences, and products.
Identify the conjugate of a complex number and use this as a computational aid, e.g., to find a quotient of complex numbers.
Represent complex numbers in the complex plane.
To add and subtract complex numbers geometrically.
Multiply complex numbers in polar form.

Students understand that:

Different representations of mathematical concepts (e.g., algebraic and geometric representation of complex numbers) reveal different features of the concept and each may facilitate computation and sense making in different settings.
Mathematics is a coherent whole and structure within mathematics allows for procedures from one area to be used in another (e.g., coordinate geometry and the complex plane, vectors and complex numbers, or plotting of a conjugate of a complex number in transformational geometry).

Example: $(-1 + \sqrt{3i})^3 = 8$ because $(-1 + \sqrt{3i})$ has modulus 2 and argument $120^{\circ}$.