Ira S. answered • 09/23/14
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The way I always do this is by first looking at the angle the given point forms when drawing the radius to the origin. This point forms a 60 degree angle in standard position. then keep adding 120 (360/3) until you get something coterminal with 60. The hypotenuse of your original triangle is 1, so 1 unit from the origin going in the 180 degree direction gives you the point -1 + 0i or -1. Going 1 unit in the 300 degree direction gives you the point 1/2 - (sqrt 3)i/2.
Hope this makes some sense to you. Look up DeMoivre's Theorem if it doesn't.
Ira S.
Have you learned the polar form of complex numbers? a+bi is rectangular form which can be converted to r(cosø + i sinø). A biproduct of DeMoivres theorem is that all the roots of an equqation form a regular polygon, square, equilateral
triangle....you can keep adding multiples of 360/n, n being the number of sides of the quadrilateral and you'll get the vertices of that regular polygon.
You're first point was 1/2 + i (sqrt3)/2. This, as a triangle has legs 1/2, sqrt3/2 and you can figure out the hypotenuse is 1. you can also figure out the angle is 60. So another way of writing this is 1(cos 60 + i sin 60). now 360/3 is 120...so keep
on adding 120s.
1(cos 180 + i sin 180) is next and then finally 1(cos 300 + i sin 300). your answer is 1(cos 180 + i sin 180) which is -1 + 0i = -1.
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09/23/14
Shivam D.
yeah i got it..thank you sir. but sir why in question it is given mode z=1/2?
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09/23/14
Shivam D.
thanks a ton mam, thanks for the explaination
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09/23/14
Minakshi D.
09/23/14