Please teach me determinants and complex numbers

For a 2x2 matrix:
A = [[a, b], [c, d]]
The determinant, denoted as det(A) or |A|, is calculated as:
det(A) = ad - bc

For a 3x3 matrix:
B = [[a, b, c], [d, e, f], [g, h, i]]
The determinant is calculated as:
det(B) = a(ei - fh) - b(di - fg) + c(dh - eg)

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' is the real part, 'b' is the imaginary part, and 'i' is the imaginary unit, defined as √(-1).

• Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
• Subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i
• Multiplication: (a + bi) × (c + di) = (ac - bd) + (ad + bc)i
• Division: (a + bi) / (c + di) = [(a + bi) × (c - di)] / [(c + di) × (c - di)] = [(ac + bd) + (bc - ad)i] / (c² + d²)