Q. 423.5( 2 Votes )
Mark the Correct alternative in the following:
Which of the following is correct for any two complex numbers z1 and z2?
A. |z1 z2| = |z1| |z2|
B. arg(z1 z2) = arg(z1) arg (z2)
C. |z1 + z2| = |z1| + |z2|
D. |z1 + z2| ≥ |z1| + |z2|
Answer :
Let, z1= r1eiα and z2 = r2eiβ
|z1| = r1 and |z2| = r2
Option A
z1z2 = r1r2ei(α+β)
|z1z2| = r1r2 = |z1| |z2|
Option A correct
Option B
arg(z1z2) = α + β
= arg(z1) + arg(z2)
Option B not correct
Let, z1 = a+ ib and z2 = c + id
Option C
z1 + z2 = (a+c) + i(b+d)
We cannot say anything about option c and option d
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