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Question Number 9836 by tawakalitu last updated on 06/Jan/17
Prove that. ∣z_1 + z_2 ∣ ≤ ∣z_1 ∣ ∣z_2 ∣
Provethat.∣z1+z2∣⩽∣z1∣∣z2∣
Commented by FilupSmith last updated on 07/Jan/17
∣z_1 ∣∣z_2 ∣≤∣z_1 z_2 ∣ ∣z_1 +z_2 ∣≤∣z_1 z_2 ∣ z_2 =z_1 +n ∣z_1 +z_2 ∣=∣2z_1 +n∣≤∣z_1 z_2 ∣ ∣2z_1 +n∣≤∣z_1 z_2 ∣ working thinking
∣z1∣∣z2∣⩽∣z1z2∣∣z1+z2∣⩽∣z1z2∣z2=z1+n∣z1+z2∣=∣2z1+n∣⩽∣z1z2∣∣2z1+n∣⩽∣z1z2∣workingthinking
Commented by prakash jain last updated on 08/Jan/17
z_1 =1 z_2 =0 ∣z_1 +z_2 ∣=∣1+0∣=1 ∣z_1 ∣∣z_2 ∣=0 ∣z_1 + z_2 ∣ ≰ ∣z_1 ∣ ∣z_2 ∣
z1=1z2=0∣z1+z2∣=∣1+0∣=1∣z1∣∣z2∣=0∣z1+z2∣⪇∣z1∣∣z2∣
Commented by prakash jain last updated on 08/Jan/17
The question should be ∣z_1 +z_2 ∣≤∣z_1 ∣+∣z_2 ∣
Thequestionshouldbe∣z1+z2∣⩽∣z1∣+∣z2∣

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