I dont understand what this problem wants so can someone please help explain it... sqrt means square root of ...

what is the magnitude and argument of (-1+sqrt3i)^2

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- Jul 15th 2008, 06:53 AMcruxkittymagnitude and argument
I dont understand what this problem wants so can someone please help explain it... sqrt means square root of ...

what is the magnitude and argument of (-1+sqrt3i)^2 - Jul 15th 2008, 07:38 AMearboth
- Jul 15th 2008, 08:26 AMIsomorphism

I assume you mean

__MAGNITUDE:__

Magnitude of a complex number is denoted by and is defined as

Geometrically, that is, on the Argand plane, this denotes the distance of the complex number from the origin.

__ARGUMENT:__

Argument of a complex number is denoted by and is defined as

Where and sgn is the signum function.

Geometrically, that is, on the Argand plane, this denotes the angle made by the line joining the origin and the complex number with the positive direction of the x axis.

__Aliter:__

If you know cube roots of unity and their positions in th argand plane.

Then observe that

Thus the complex number is .

But we know that the cube roots of unity are on the unit circle and that they are distributed over the unit circle at to each other. 1 is on the real line. is at an angle to the x-axis. is at an angle to the x-axis.

Mathematically they mean

Lets use these facts:

- Jul 15th 2008, 08:40 AMPlato
Note the correction above.

I am sure that the question deals with this number: .

“Multitude” must mean absolute value (distance from origin): .

The argument is the angle the ray from the origin through the number makes with the positive real axis.

In doing this problem here are two useful facts: .