Saturday, August 17, 2013

`sqrt(48)[cos(-30^@) + i sin(225^@)]` Write the standard form of the complex number. Then represent the complex number graphically.

Standard form of complex number is ` ` were ` ` To write the number in standard form we first need to calculate the values of trigonometric functions for the given angle.


`cos(-30^circ)=cos 30^circ=sqrt 3/2`


`sin 225^circ=-sin 45^circ=-sqrt2/2`


We will also write `sqrt48` as `4sqrt3.`              


Therefore, we get


`sqrt48(cos(-30^circ)+i sin (225^circ))=`


`4sqrt3(sqrt3/2-(isqrt2)/2)=`


`2cdot3-2isqrt6=`


`6-2sqrt6i` <--Solution            

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