Given two complex numberZ1-7-3-7i and Z2-9-9-3iThe argument of Z1 Z2 in degree is

nbsp;Argument(Z_1) =θ_1=tan^ 1 ( nbsp; 7√(3)7 ) θ_1=tan^ 1(tan60^∘) ⇒θ _1 =60^∘ Argument(Z_2)=θ _2 =tan^ 1 ( 9√(3)9 ) θ _2 =tan^ 1(tan60^∘) ⇒θ _2 = 60^∘ Ar ...

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Engineering Mathematics

Basic Properties

Given two com...

Question

Given two complex number
$Z_{1} = \frac{7}{\sqrt{3}} + 7 i a n d Z_{2} = 9 + (9 \sqrt{3}) i$
The argument of $Z_{1} Z_{2}$ (in degree) is

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150

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120

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180

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Solution

The correct option is C 120
$Argument (Z_{1}) = θ_{1} = t a n^{- 1} (\frac{7 \sqrt{3}}{7})$
$θ_{1} = t a n^{- 1} (t a n 60^{\circ})$
$\Rightarrow θ_{1} = 60^{\circ}$
$Argument (Z_{2}) = θ_{2} = t a n^{- 1} (\frac{9 \sqrt{3}}{9})$
$θ_{2} = t a n^{- 1} (t a n 60^{\circ})$
$\Rightarrow θ_{2} = 60^{\circ}$
$Argument (Z_{1} Z_{2}) = Argument (Z_{1}) + Argument (Z_{2})$
$= 60^{\circ} + 60^{\circ}$
$\Rightarrow = 120^{\circ}$

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Given two complex number Z1=7√3+7i and Z2=9+(9√3)i The argument of Z1Z2 (in degree) is

The correct option is C 120 Argument(Z1)=θ1=tan−1(7√37) θ1=tan−1(tan60∘) ⇒θ1=60∘ Argument(Z2)=θ2=tan−1(9√39) θ2=tan−1(tan60∘) ⇒θ2=60∘ Argument(Z1Z2)= Argument(Z1)+ Argument(Z2) =60∘+60∘ ⇒ =120∘

Given two complex number
$Z_{1} = \frac{7}{\sqrt{3}} + 7 i a n d Z_{2} = 9 + (9 \sqrt{3}) i$
The argument of $Z_{1} Z_{2}$ (in degree) is