How do you write 2+3i in polar form?

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- Dec 9th 2010, 08:56 AMmariasmiles25How do you write 2+3i in polar form?
How do you write 2+3i in polar form?

- Dec 9th 2010, 09:03 AMUnknown008
The polar form has the general form

Where r is the modulus of the complex number and theta the argument of the complex number. (Smile) - Dec 10th 2010, 02:40 AMHallsofIvy
The complex number 2+ 3i is represented by the point (2, 3) in the complex plane. The "modulus" unknown008 refers to is the distance from (0, 0) to (2, 3) which is and the "argument" is the angle the line from (0, 0) to (2, 3) makes with the positive x-axis. That line forms the hypotenuse of a right triangle with "opposite side" the y value, 3, and "near side" the x value, 2. The angle, , is given by .

You can derive those relations directly from . We must have and . Square each and add and you get . Divide the second equation by the first and you get .