Let
z1=x1+iy1
and
z2=x2+iy2
and z2 is nonzero complex number.
Then the quotient
is given by
Example 1.
If
z1 = 2 + 3i
and
z2 = 4 + 5i,
find
.
Solution
We have
x1 = 2,
y1 = 3,
x2 = 4,
y2 = 5.
Hence, by definition,
=
=
To express as a single complex number the quotient of one complex number as
z1=x1+iy1
by another complex number, as
z2=x2+iy2
, where
z2
does not equal 0, multiply both numerator and denominator of the indicated quotient
by
x2 - iy2
, the conjugate of the denominator:
=
=
=
=
Illustration (compare with Example 1).
If
z1 = 2 + 3i
and
z2 = 4 + 5i
,
find
.
=
=
=
=
=
=
=
Conjugate of the Quotient of Complex Numbers
The conjugate of the quotient of complex numbers equals to the quotient of the conjugate
of these complex numbers. In formula