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complex numbers

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Hi all. I have that long of vector is z = 2i, then tangent of phi is 2/0, and dividing by zero is not allowed. I must be missing something. So what is the value of a and b? Thanks

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I assume you want to write it in polar coordinates.

If you think about it, draw the number in the complex plane, I'm sure you'll see that the angle is 90 degrees, i.e. pi/2 radians. Another way is to know the limits of tangens: lim a->inf ( tan( a / 2 ) ) = pi/2. Use a pocket calculator to draw the tan( x / 2 ) function if you're not convinced.

The Magnitude is just the euclidean distance of the real and imaginary parts.

mag = | real^2 + imag^2 | , in this case obviously equal to 2.

Thus in polar coordinates your number is:

2*exp(i*pi/2)

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