Consider the diagram of the powers, z^n , of the complex number z=r\, ext{cis}( heta) shown below. In the diagram z is in the first quadrant, and successive powers of z , labelled z_1, z_2, z_3 and z_4 , are positioned anticlockwise from z , on a circle centred at the origin, with radius r .
Using this diagram, choose the following statements that are correct.

Question

Consider the diagram of the powers,   z^n , of the complex number   z=r\,	ext{cis}(	heta)  shown below.  In the diagram   z  is in the first quadrant, and successive powers of   z , labelled   z_1, z_2, z_3  and   z_4 , are positioned anticlockwise from   z , on a circle centred at the origin, with radius   r .   
 Using this diagram, choose the following statements that are correct.

Answer

As the powers of   z  follow an anticlockwise path, we can say that the values of   n  are positive integer values.

Answer

We cannot determine if the integer values of   n  are positive or negative.

Answer

We cannot determine   r  from the diagram.

Answer

We can see that   r=1  as the magnitude of the powers of   z  is neither increasing nor decreasing.

Answer

As the powers of   z  follow an anticlockwise path, we can say that the values of   n  are negative integer values.

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Consider the diagram of the powers, z^n , of the complex number z=r\,\text{c...

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