PC.NCNS: Complex Number System

Complex Number System

PC.NCNS.2Use the relation i^2=−1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.PC.NCNS.3Find the conjugate of a complex number in rectangular and polar forms and use conjugates to find moduli and quotients of complex numbers.PC.NCNS.4Graph complex 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.PC.NCNS.5Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.PC.NCNS.6Determine the modulus of a complex number by multiplying by its conjugate and determine the distance between two complex numbers by calculating the modulus of their difference.PC.NCNS.7Solve quadratic equations in one variable that have complex solutions.PC.NCNS.8Extend polynomial identities to the complex numbers and use DeMoivre’s Theorem to calculate a power of a complex number.PC.NCNS.9Know the Fundamental Theorem of Algebra and explain why complex roots of polynomials with real coefficients must occur in conjugate pairs.
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