Calculate (3 − 2i)(−2 + 5i).
Which of the following matrices are Hermitian? A = [2 3 – i 3 + i 4], B = [1 2i -2i 3 – i], C = [0 i i -i 0 i -i i 0]
Unitarily diagonalize A = [4i 1 + 3i -1 + 3i i].
Unitarily diagonalize A = [4 1 -i 1 4 -i i i 4].
Unitarily diagonalize A = [2 1 + i 1 – i 3].
Are the matrices U = [1 -i i 1] and V = [1/√3(1 + i) 1/√6(1 + i) – 1/√3i 2/√6i] unitary?
Let A = [5 -6 3 -1]. Find its eigenvectors and diagonalize over C.
Determine whether B = [2 i i 4] is diagonalizable over C.
Calculate the following using the polar form. (a) (2 + 2i)^3 (b) (2i)^3 (c) (√3 + i)^5
Use de Moivre’s Formula to calculate (2 + 2i)^3.
Calculate (1 − i)(− √3 + i) and 2 + 2i / 1 + √3i using polar form.