Complex Numbers Quick Reference
By Dr. Iris Vaughan, Mathematics Editor·Published 10 December 2025·Last reviewed 30 January 2026
Complex number operations (addition, multiplication, conjugate, modulus, argument), Euler's formula, and de Moivre's theorem.
Key Formulas
(a+bi)+(c+di)=(a+c)+(b+d)i
(a+bi)(c+di)=(ac−bd)+(ad+bc)i
Conjugate: a+bi→a−bi
Modulus: |z|=√(a²+b²)
Euler: e^(iθ)=cosθ+i sinθ
de Moivre: (cosθ+i sinθ)ⁿ=cos(nθ)+i sin(nθ)
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