Q. 423.5( 2 Votes )

# Mark the Correct alternative in the following:

Which of the following is correct for any two complex numbers z_{1} and z_{2}?

A. |z_{1} z_{2}| = |z_{1}| |z_{2}|

B. arg(z_{1} z_{2}) = arg(z_{1}) arg (z_{2})

C. |z_{1} + z_{2}| = |z_{1}| + |z_{2}|

D. |z_{1} + z_{2}| ≥ |z_{1}| + |z_{2}|

Answer :

Let, z_{1}= r_{1}e^{iα} and z_{2} = r_{2}e^{iβ}

|z_{1}| = r_{1} and |z_{2}| = r_{2}

__Option A__

z_{1}z_{2} = r_{1}r_{2}e^{i(α+β)}

|z_{1}z_{2}| = r_{1}r_{2} = |z_{1}| |z_{2}|

Option A correct

__Option B__

arg(z_{1}z_{2}) = α + β

= arg(z_{1}) + arg(z_{2})

Option B not correct

Let, z_{1} = a+ ib and z_{2} = c + id

__Option C__

z_{1} + z_{2} = (a+c) + i(b+d)

We cannot say anything about option c and option d

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