Question

State and prove the triangle inequality of complex numbers.​

Answer 1

Answer:

Proof 1. Let z1=a1+ia2,z2=b1+ib2. Then from the definition of the modulus, the above equation translates into: ((a1+b1)2+(a2+b2)2)12≤(a12+a22)12+(b12+b22)12.

Answer 2

Answer:

Proof 1. Let z1=a1+ia2,z2=b1+ib2. Then from the definition of the modulus, the above equation translates into: ((a1+b1)2+(a2+b2)2)12≤(a12+a22)12+(b12+b22)12.