SOLUTION: Find all solutions of the equation {{{ x^4 - 625i = 0 }}} and represent the solutions graphically. Ty!

Algebra ->  Test -> SOLUTION: Find all solutions of the equation {{{ x^4 - 625i = 0 }}} and represent the solutions graphically. Ty!      Log On


   

Question 1076611: Find all solutions of the equation +x%5E4+-+625i+=+0+ and represent the solutions graphically. Ty!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions of the equation x^4 - 625i = 0 and represent the solutions graphically.
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x = 625^(1/4)[cos(0+360n)/4]+i*sin(0+360n)/4)
If n = 0, x = 5[cos(0)+isin(0)] = 5[1+i*0] = 5
If n = 1, x = 5[cos(90)+isin(90)] = 5[[0+i*1] = 5i
If n = 2, x = 5[cos(180)+isin(180)] = 5[-1+i*0] = -5
If n = 3, x = 5[cos(270)+isin(270)] = 5[0-i] = -5i
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Graphical solution:
Let the x axis be Real ; Let the y axis be Imaginary
Plot points at (5,0),(0,5),(-5,0),(0,-5)
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Cheers,
Stan H.
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