a planar vector can be represented in terms of its magnitude and angle using a complex
exponential pattern
Cartesian notation and vector representation:
xy pairs
a
1
3
⎛
⎝
⎞
⎠
:=
a vector with x=1 and y=3
b
2
5
⎛
⎝
⎞
⎠
:=
a vector with x=2 and y=5
calculate the vector magnitudes
a
3.162
=
1
2
3
2
+
3.162
=
b
5.385
=
2
2
5
2
+
5.385
=
calculate the angle of the planar vector using the arctangent function
atan
3
1
⎛
⎝
⎞
⎠
1.249
=
atan
3
1
⎛
⎝
⎞
⎠
71.565 deg
⋅
=
atan
5
2
⎛
⎝
⎞
⎠
1.19
=
atan
5
2
⎛
⎝
⎞
⎠
68.199 deg
⋅
=
Now use complex number notation to represent the same vectors
A13
i
+
:=
B25
i
+
:=
Use the REAL and IMAGINARY functions to extract the x and y values.
Re A
() 1
=
Im A
() 3
=
Re B
() 2
=
Im B
() 5
=
Calculate magnitudes
magA
A
3.162
=
:=
magB
B
5.385
=
:=
Calculate the angles using the ARG function
argA
arg A
( )
1.249
=
:=
argB
arg B
( )
1.19
=
:=
Now use complex Exponential notation to represent the same vectors
Using Complex Numbers to Represent Planar
Vectors  in MathCad
MAG e
i ANGLE
⋅
⋅
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 Fall '11
 staff
 Complex number, vector representation, Planar vector, Complex Exponential vector

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