Thursday, May 27, 2010

`4` Write the trigonometric form of the number.

To convert 4 to trigonometric form, express it in z=x+yi form. So it becomes:


`z=4+0i`


Take note that the trigonometric form of a complex number z=x+yi is


`z=r(cos theta + isin theta )`


where 


`r= sqrt(x^2+y^2)`     and     `theta = tan^(-1) y/x`


Applying these two formulas, the values of r and theta of z=4+0i are:


`r=sqrt(4^2+0^2)=4`


`theta = tan^(-1) 0/4 =0^o`


Plugging them to the trigonometric form of a complex number result to:


`z= 4(cos0^o + isin 0^o)`



Therefore, the trigonometric form of 4 is  `4(cos 0^o + isin 0^o)` .

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