For the complex number 3 + 4i, what is the absolute value and the argument? Is it not tan (4/3)?  

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A complex number z = x + yi, can be expressed as a line with a length equal to |z| or sqrt (x^2+ y^2). The line makes an angle A with the positive x-axis that is known as its argument and equal to A= arc tan (y/x).  The argument is kept a positive angle by the use of either adding or subtracting pi radians from arc tan (y/x).

For the complex number 3 + 4i, the absolute value is sqrt (3^2 + 4^2) = sqrt (9 + 16) = sqrt 25 = 5.

The argument is arc tan (4/3), which is equal to 0.9273 radians, and the absolute value is 5.

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