Algebra
Complex Numbers
What is
\[\large i^2 +i^6 +i^4?\]
Note: \(i\) is the imaginary number \(\sqrt{-1}\).
by
Parth Lohomi
\[\displaystyle\sum_{n=0}^{1000} i^n=? \] where \(i=\sqrt{-1}\).
by
Parth Lohomi
\[\large i{ z }^{ 3 }+z^{ 2 }-z+i=0\]
For \(i = \sqrt{-1}\), \(z\) is a complex number that satisfies the equation above. What is the value of \(\left| z \right| \)?
by
shivamani patil
Evaluate
\[\large{ \frac { { (1+i) }^{ 85 } }{ { (1-i) }^{ 83 } }}\]
Hint: There's an extremely fast way to solve this if you know why
\(\large 1+i = \sqrt{2}e^{i{\pi}/{4}} \)
by
Abdulrahman El Shafei
Can you evaluate this giant power of \(i\)?
\[\huge i^{-9999}\]
by
Aman Baser