I would like to know what is the square root of i , and i squared? I am looking for a response appropriate for secondary level students.
|Complex numbers can be written in the form a+ib where a and b are real numbers. This gives rise to a graphical way to represent complex numbers in what is called the complex plane. Draw a coordinate system as you would for the Cartesian plane but label the horizontal axis the real axis and the vertical axis the imaginary axis. The complex number a+ib is then representated in the complex plane by the point with coordinates (a,b).|
For points on the unit circle (points at a distance 1 from 0) you can use some trigonometry to get a particularly useful representation. For a point z on the unit circle measure the angle (counterclockwise) between the positive real axis and the line segment joining z to 0. This angle, written , is called the argument of z and then . Now what happens when you multiply two such numbers? If
then,expanding as you normally would, using the fact that i squared is -1 and using the double angle expressions for sine and cosine, gives
Hence is the complex number on the unit circle with argument
Now back to your questions.
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