Monday, November 14, 2016

`8 + 3i` Write the trigonometric form of the number.

`8+3i`


The trigonometric form of a complex number `z=x+yi` is


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


where 


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


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


Applying these formulas, the values of r and theta of z=8+3i are:


`r= sqrt(8^2+3^2)=sqrt(64+9)=sqrt73`


`theta = tan^(-1) 3/8=20.56`


Plug-in them to the trigonometric form.


`z=sqrt73(cos 20.56^o+isin20.56^o)`



Thus, the trigonometric form of  `8+3i`  is  `sqrt73(cos20.56^o + isin20.56^o)` .

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