Convert the following to polar form, answer in radians
(i) 1 + j3
(ii)5 - j2
In general, the picture of a + jb is the vector that
connects the origin (0,0) to the point (a,b)
Therefore, the picture of 1 + j3 is the vector that
connects the origin to the point (1,3) is this vector:
Now we draw in the y-coordinate:
That triangle has base 1, and the green side is 3, so the vector is
the hypotenuse and that equals
_____ ___ __
Ö1²+3² = Ö1+9 = Ö10
The angle between the vector and the x-axis has a tangent of 3/1, so
the angle is 1.249 radians, approximately. So the polar form can be
written any of the following ways:
__
Ö10[sin(1.249) + j·cos(1.249)]
__
Ö10 cjs(1.249)
__
Ö10 Ð 1.249
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(ii)5 - j2
The picture of 5 - j2 is the vector that
connects the origin to the point (5,-2) is this vector:
Now we draw in the y-coordinate:
That triangle has top side 5, and the green side is -2, so the vector
is the hypotenuse and that equals
________ ____ __
Ö5²+(-2)² = Ö25+4 = Ö29
The angle between the vector and the x-axis has a tangent of -2/5, so
the angle is -.381 radians, approximately. So the polar form can be
written any of the following ways:
__
Ö29[sin(-.381) + j·cos(-.381)]
__
Ö29 cjs(-.381)
__
Ö29 Ð -.381
Edwin
