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1st write 1+ i in polar form, sketch a diagram to find the angle ( =pi/4) and find the modulus ( sqrt(2))z^3 = Sqrt(2) E^ipi/4This is true for all equivalent solutions (add 2kpi) z^3 = sqrt(2)e^(pi/4 +2kp...

To start off, It's worth noting the definition of eigenvalues: for a Matrix A (n x n), it's ith eigenvalue (λ_i) is defined as the scalar constant the ith eigenvector (v_i) is multipli...

The general solution y_GS(t) to a differential equation in the form ay''(t)+by'(t)+cy(t)=f(t) is the sum of the complementary function y_CF(t) and a <...

Need whiteboard throughout to properly answer, so will go through the ideas of what to do:

Take the base case of when n=1, and show that            (sum from 1 to 1) j = n(n+1)/2       is equal to ...

Simplify i⁴?

We know that i = -1^1/2

Therefore i²=-1

As i⁴=i²xi² 

Then i⁴=-1x-1=1