Unpacked Content
Knowledge
Students know:
- The definition of the conjugate of a complex number.
- A complex number divided by itself equals 1.
- The product of a complex number and its conjugate is a real number (the square of the modulus).
Skills
Students are able to:
- Find the conjugate of a complex number.
- Find the modulus of a complex number
- Find the product of two complex numbers.
- Find (simplify) the quotient of complex numbers.
Understanding
Students understand that:
- The conjugate of a complex number differs by the sign of its imaginary part and has the same modulus.
- The modulus of a complex number corresponds to the magnitude of a vector and, therefore, is useful in the geometric representation of complex numbers.
- Mathematical convention is that radical expressions are not left in denominators to facilitate numerical approximations. therefore, since the i is equal to the square root of -1, conventional form says that i does not appear in the denominator of a fraction.
- Different forms of a complex number quotient (indicated quotient, single complex number) may be more useful for various purposes.
Vocabulary
- Conjugate
- Complex number
- Modulus/Moduli
