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find the four complex fourth roots of w=1 and plot them.

Mathematics
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Apr 17th, 2015

The fourth roots of 1 are 1, -1, i and -i. We can check this easily. So the correct picture is C (all roots lie at the axis with the coodinates of ±1).

Now, fill out the empty fields at a top of the question. The 1 as a complex number has an angle of 0. So,

the roots are:      cos([0 + (2π)*k]/4) + i*sin([0 + (2π)*k]/4),  k = 0,1,2,3.  (4 pcs)

2π/4 = π/2 = 90°   (/4 is from the fourth degree).  So,

the roots are:    cos(0°+90°k) + i*sin(0°+90°k) = cos(90°k) + i*sin(90°k),  k=0,1,2,3.

Apr 17th, 2015

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