Friday, August 10, 2012

`1 + i` Write the trigonometric form of the number.

To convert a complex number



to its trigonometric form


`z=r(cos theta + isintheta)`


the formulas needed are:


`r=sqrt(x^2+y^2)`


`theta = tan^(-1) y/x`


Applying these two formulas,  the r and `theta` of 


`z=1+i`


will be:


`r = sqrt(1^2+1^2) = sqrt2`


`theta = tan^(-1) (1/1)=tan^(-1) 1 = 45^o`


Plugging them to 


`z=r(costheta+ isin theta)`


result to:


`z=sqrt2(cos45^o + isin45^o)`



Therefore, the trigonometric form of  `1+i`   is   `sqrt2(cos45^o+isin45^o)` .

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