Question

$\left|\begin{array}{ccc}1+i& 1-i& 1\\ 1-i& i& 1+i\\ i& 1+i& 1-i\end{array}\right|$ is a

• A. real number
• B. irrational number
• C. complex member
• D. Purely imaginary

Answer 1

Answer: (C)

complex member

$1+i\left[i\right(1-i)-(1+i{)}^2]-(1-i)\left[\right(1-i{)}^2-i(1+i)]+1\left[\right(1-i\left)\right(1+i)-i^2]$
$=(1+i)[1-l^2-2i]-(1-i)[1+l^2-2i-i-l^2]+[1-l^2-l^2]$
$=(1+i)[-2i^2-2i]-(1-i)(1-3i)+[1-2i^2]$
$=(1+i)[+2-2i]-(1-i)(1-3i)-1$
$2[1-l^2]-(1-i)(1-3i)-1$
$4-(1-3i-i+3i^2)-1$
$3-(1-4i-3)$
$3-(-2-4i)$
$=5+4i$
so (c) complex number