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= r1e and z2 = r2e

|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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