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ModulusFind the argument and the modulus of the complex number z = 1+i*3^1/2
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The absolute value of the complex number can be evaluated when we know the rectangular form of z:
z = x + i*y
|z| = sqrt(x^2 + y^2)
We'll identify the real part and the imaginary part of z:
x = Re(z) = 1
y = Im(z) = sqrt 3
Now, we'll calculate the absolute value:
|z| = sqrt[1^2 + (sqrt3)^2]
|z| = sqrt (1+3)
|z| = sqrt 4
|z| = 2
The modulus of the given complex number is |z| = 2.
The argument of the complex number is the angle to x axis made by the vector of position of the complex number.
arg(z) = a
tan a = y/x
tan a = sqrt 3/1
tan a = sqrt 3
a = pi/3 + k*pi
arg(z) = pi/3 + k*pi
Posted by giorgiana1976 on May 31, 2011 at 2:04 PM (Answer #2)
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