Roots of unity
This content delves into the concept of roots of unity, specifically when raised to the power of n equals 1 or -1. It discusses implications for different values of n and how they relate to the variable r. Through visual representations and explanations, the solutions to these equations are explored in detail, shedding light on the properties of roots of unity in mathematical contexts.
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Presentation Transcript
Roots of unity rn = 1
We will also solve rn = -1
?2= 1 implies r = 1 1 2= 2? ? 2 Roots of unity rn = 1
?2= -1 implies r = ( 1) 1 2= 1+2k ?/2
?3= 1 implies r = 1 1 3= 2? ? 3 Roots of unity rn = 1
?3= -1 implies r = ( 1) 1 3= 1+2k ?/3
?4= 1 implies r = 1 1 4= 2? ? 4 Roots of unity rn = 1
?4= -1 implies r = ( 1) 1 4= 1+2k ?/4
?5= 1 implies r = 1 1 5= 2? ? 5 Roots of unity rn = 1
?5= -1 implies r = ( 1) 1 5= 1+2k ?/5