In addition to the trig functions, there are other functions that take complex arguments.
ABS(<real>) or ABS(<complex>)
The absolute function, which is found on the keyboard above the left
bracket key, returns the absolute value of a real number.
Eg.
ABS(-3)
returns a value of 3.
When you use the absolute function on a complex number
a + bi
it returns the magnitude of the complex
2
number as
a
+
b
2
. Note the requirement for double brackets in this case. The outer pair are those of the
function
ABS(…)
. The inner pair are those of the number in
(a,b)
format.
SIGN(<real>) or SIGN(<complex>)
This function is found in the Real group not the Complex group but is
very useful with complex numbers and so is also covered here. If given
a vector/complex number
(a,b)
,
SIGN
will return another
vector/complex number which is a unit vector in the direction of
(a, b).
Note again the requirement for doubled brackets.
⎛
a
b
⎞
i.e.
SIGN((A,B))
returns
⎜⎜
,
⎟⎟
.
2
2
⎝
a
+
b
2
a
+
b
2
⎠
y
This is very useful, not just in complex numbers, but also in vector problems.
6
See also:
SIGN
(in the Real group),
IM
,
RE
,
ARG
,
CONJ
4
2
27
o
ARG(<complex>) or ARG(<vector>)
x
– 2
2
4
6
– 2
This function, also found on the keyboard, returns the size of the angle
defined by regarding the complex number as a vector. For example
D
ARG
(
4+2i
) would be
26 565
. The same information can, of course, be
⋅
obtained using trig. The result is dependent on the current angle setting
in
MODES
. Again, note the requirement for doubled brackets. Using
ARG(a+bi)
instead avoids this requirement.
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