Math Editor

COMPLEX NUMBER

• Algebra of Complex number

1. a+ib=c+id⇔a=cand b=d
2. (a+ib)+(c+id)=a+c+i(b+d)
3. (a+ib)−(c+id)=a−c+i(b−d)
4. Additive identity =0=0+i0
5. Additive inverse =a+ib=−a−ib
6. (a+ib)(c+id)=(ac−bd)+i(bc+ad)
7. c+ida+ib​=c2+d2(a+ib)(c−id)​
8. Multiplicative identity =1=1+0i
9. Multiplicative inverse of a+ib=a+ib1​=a2+b2a−ib​

10.√a√b=√ab if and only if at least one of

a and b is non-negative