Algebraic Identities of Complex Numbers

All the algebraic identities apply equally for complex numbers. The addition and subtraction of complex numbers and with exponents of 2 or 3 can be easily solved using algebraic identities of complex numbers.

• (z1+z2)2=z21+2z1z2+z22(z1+z2)2=z12+2z1z2+z22
• (z1−z2)2=z21−2z1z2+z22(z1−z2)2=z12−2z1z2+z22
• (z1+z2)3=z31+3z21z2+3z1z22+z32(z1+z2)3=z13+3z12z2+3z1z22+z23
• (z1−z2)3=z31−3z21z2+3z1z22−z32(z1−z2)3=z13−3z12z2+3z1z22−z23
• (z1+z2)(z1−z2)=z21−z22(z1+z2)(z1−z2)=z12−z22
• (z1+z2+z3)2=z21+z22+z23+2z1z2+2z2z3+2z3z1