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Question
If |z1| = |z2|, is it necessary that z1 = z2?
Sum
Solution
|z1| = |z2|
z1 & z2 are at the some distance from origin.
Consider, z1 = 3 + 4i & z2 = 4 + 3i
|z1| = |3 + 4i| = `sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt25 = 5`
|z2| = |4 + 3i| = `sqrt(4^2 + 3^2) = sqrt(16 + 9) = 5`
z1 ≠ z2
Hence, If |z1| = |z2|, then it is not necessary that z1 = z2.
shaalaa.com
Concept of Complex Numbers - Algebra of Complex Numbers - Equality
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