Question

If z1 , z2 are two complex numbers then : |z1+z2| ? |z1|+|z2| |z1+z2| = |z1|+|z2| ||z1|-|z2|| > |z1-z2| ||z1|-|z2|| ? |z1-z2|

          If z1 , z2 are two complex numbers then :

|z1+z2| ? |z1|+|z2|
|z1+z2| = |z1|+|z2|
||z1|-|z2|| > |z1-z2|
||z1|-|z2|| ? |z1-z2|

Added by Mohamed C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/26/2023

Step 1

Given two complex numbers $z_1$ and $z_2$, we want to show that: $$|z_1 + z_2| \leq |z_1| + |z_2| \leq |z_1 - z_2| + |z_1| + |z_2|$$ We can use the triangle inequality to show the first part: $$|z_1 + z_2| \leq |z_1| + |z_2|$$ Now, let's show the second Show more…

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If [z] are two complex numbers, then |z1+2z2| ≤ |z1|+|z2| |z1+2z2| ≤ |z1|+|z2| |z1-z2| ≤ |z1|+|z2| |z1-z2| ≤ |z1|+|z2| |z1-z2|^4 ≤ |z1|^4+|z2|^4 |z1-z2|^2 ≤ |z1|^2+|z2|^2