Trigonometric Form Of A Complex Number
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36.5:
Trigonometric
Form
of
a
Complex
Number
Objective:
To
write
complex
numbers
in
trigonometric
form
and
to
find
products
in
trigonometric
form.
In
order
to
represent
complex
numbers
geometrically,
you
use
an
Argand
Diagram
to
represent
the
complex
plane.
To
represent
the
complex
number
3 + 4i ,
it
can
be
drawn
as
the
point
(3,4)
or
by
an
arrow
from
the
origin
to
(3,4).
The
absolute
value
of
a
complex
number
a + bi
is
defined
as
the
distance
between
the
origin
and
the
point
(a,b).
€
Definition:
_____________________________________________________
€
Example
#1:
Plot
z = −1− 2i
and
find
its
absolute
value.
€
The
trigonometric
form
of
a
complex
number
z = a + bi
is
given
by
________________________________
where
r = _________________________
a = _____________________,
b = ___________________________
and
tan θ = _________________________
€
Example
#2:
Express
−1− 2i
in
trigonometric
form.
€
€
€
1.
Find
r.
2.
Find
θ .
3.
Answer
€
€
€
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