If z1 - 170- and z2 -70- then the principal argument of z1 z2 is

Given: (z_1) = 170^∘ and (z_2) =70^∘ (z_1 z_2) =(z_1) + (z_2)+2kπ,k∈ℤ ⇒(z_1 z_2)= 170^∘ + 70^∘+2k(180^∘) nbsp; ⇒(z_1 z_2)=240^∘+2k(180^∘) If k= 1 ⇒(z_1 z_ ...

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Byju's Answer

Standard XIII

Mathematics

Properties of Argument

If z1 = 170∘ ...

Question

If $arg (z_{1}) = 170^{\circ}$ and $arg (z_{2}) = 70^{\circ}$ , then the principal argument of $z_{1} z_{2}$ is

120^{\circ}

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- 120^{\circ}

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240^{\circ}

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- 240^{\circ}

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Solution

The correct option is B $- 120^{\circ}$
$arg (z_{1} z_{2}) = arg (z_{1}) + arg (z_{2}) + 2 k π, k \in Z$
$= 170^{\circ} + 70^{\circ} + 2 k π$
$= 240^{\circ} + 2 k π$
If $k = - 1$
$arg (z_{1} z_{2}) = 240^{\circ} - 2 π = 240^{\circ} - 360^{\circ} = - 120^{\circ} \in (- π, π]$
$∴$ principal argument $= - 120^{\circ}$

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If arg(z1)=170∘ and arg(z2)=70∘, then the principal argument of z1z2 is

The correct option is B −120∘ arg(z1z2)=arg(z1)+arg(z2)+2kπ,k∈Z =170∘+70∘+2kπ =240∘+2kπ If k=−1 arg(z1z2)=240∘−2π=240∘−360∘=−120∘∈(−π,π] ∴ principal argument =−120∘

If $arg (z_{1}) = 170^{\circ}$ and $arg (z_{2}) = 70^{\circ}$ , then the principal argument of $z_{1} z_{2}$ is