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Simplify (i+1)^3200-(i-1)^3200
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i + 1 = = .
Now apply de Moivre's formula: = .
You will get
= = = . (1)
Similarly,
i - 1 = = .
= = = . (2)
Combining (1) and (2), you will get
(i+1)^3200-(i-1)^3200 = - = 0.
Answer. (i+1)^3200-(i-1)^3200 = 0.
There is a bunch of my lessons on complex numbers
- Complex numbers and arithmetical operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Raising a complex number to an integer power
- How to take a root of a complex number
- Solution of the quadratic equation with real coefficients on complex domain
- How to take a square root of a complex number
- Solution of the quadratic equation with complex coefficients on complex domain
in this site.