What is the induced two norm of the matrix (1-i 1+i, 1+i 1+1)

My rows are separated by the comma

This is given by the square root of the absolute value of the largest eigenvalue of A* A, where A* is the conjugate transpose of A.

Assuming that A =
[1- i 1+i]
[1+i 1+i]

A* A =
[1+i 1-i] [1- i 1+i]....[4 2+2i]
[1-i 1-i] [1+i 1+i].=.[2-2i 4].

Now, compute its eigenvalues from the characteristic equation
t^2 - 8t + 8 = 0
==> (t - 4)^2 = 8
==> t = 4 ± √8.

Hence, ||A||₂ = √(4 + √8).
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Link:
http://www.ece.uah.edu/courses/ee448/cha…

I hope this helps!