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What is
i2+i6+i4?\large i^2 +i^6 +i^4?i2+i6+i4?
Note: iii is the imaginary number −1\sqrt{-1}−1.
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∑n=01000in=?\displaystyle\sum_{n=0}^{1000} i^n=? n=0∑1000in=? where i=−1i=\sqrt{-1}i=−1.
iz3+z2−z+i=0\large i{ z }^{ 3 }+z^{ 2 }-z+i=0iz3+z2−z+i=0
For i=−1i = \sqrt{-1}i=−1, zzz is a complex number that satisfies the equation above. What is the value of ∣z∣\left| z \right| ∣z∣?
Evaluate
(1+i)85(1−i)83\large{ \frac { { (1+i) }^{ 85 } }{ { (1-i) }^{ 83 } }}(1−i)83(1+i)85
Hint: There's an extremely fast way to solve this if you know why 1+i=2eiπ/4\large 1+i = \sqrt{2}e^{i{\pi}/{4}} 1+i=2eiπ/4
Can you evaluate this giant power of iii?
i−9999\huge i^{-9999}i−9999
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