complex numbers
product
(a+bi)(c+di) is defined to be (ac−bd)+(bc+ad)i represents the______.
difference
(a+bi)−(c+di) is defined to be (a+bi)+(−c−di) represents the______.
Complex numbers
A complex number is a number which can be written in the form a+bi where a and b are real numbers and i=−1−−−√ Definition: The set of Complex Numbers is the set of all numbers which can be written in the form a+bi where a and b are real numbers and i=−1−−−√ Standard Symbol: C Symbolic Form: C={a+bi∣∣a∈R,b∈R,and i=−1−−−√}
Reducing
If the numerator and the denominator of a fraction contain common factors, the fraction is equivalent to a fraction without some of those common factors. Removing some of these common factors is called reducing the fraction The process of reducing a fraction depends on the definition of multiplication as illustrated below. abac=aabc=1bc=bc Obsserve that reducing a fraction produces a new fraction which is equivalent to the original fraction.
Polynomial p Divisible by Polynomial d
If the remainder r in the division algorithm is 0, then we say that the _______ __ ___ ___ ___ ___ _______ __
Difference of Complex Numbers
The _____ (a+bi)−(c+di) is defined to be (a+bi)+(−c−di)
Multipicitavie Inverse of a Complex Number
The ______ a+bi is its conjugate divided by its norm a−bi/a2+b2
norm
The ______ of a complex number a+bi is a2+b2.
conjugate
The ______ of a complex number a+bi is a−bi.
Quotient of Complex Numbers
The _______ (a+bi)÷(c+di) is defined to be (a+bi)(c−di/c2+d2)
sum of two complex numbers
The _______ a+bi and c+di is defined by (a+bi)+(c+di)=(a+c)+(b+d)i
multiplicative inverse
The _______ of a complex number a+bi is its conjugate divided by its norm a−bia2+b2
Product of Complex Numbers
The ________ (a+bi)(c+di) is defined to be (ac−bd)+(bc+ad)i
complex unit or the imaginary unit.
The complex number i is sometimes called the
binomials
The product of two complex numbers is best computed as the product of two______.
Reciprocal
The reciprocal of a fraction ab with numerator not zero is constructed by interchanging numerator and denominator. So the reciprocal of ab is ba The reciprocal of a fraction is important because it is the multiplicative inverse of the fraction. Note that abba=1
Norm of a Complex Number
The_____ a+bi is a2+b2.
quotient
The______ (a+bi)÷(c+di) is defined to be (a+bi)(c−di/c2+d2)
equal
Two complex numbers a + bi and c + di are _______ if a = c and b = d.
opposite
a complex number a+bi is −a−bi represents the ______.
complex number
a number that can be written in the form a+bi where a and b are real numbers and i=√−1
sum of two complex numbers
a+bi and c+di is defined by (a+bi)+(c+di)=(a+c)+(b+d)i
Conjugate of a Complex Number
a+bi is a−bi
Opposite of a Complex Number
a+bi is −a−bi.
-1
i2=
real component
of the complex number a+bi is a
