Let z and - be complex numbers such that z-i -0 and arg z - - - Then arg z equals

Z̅+i ω̅=0 ⇒z̅= i ω̅ ⇒ z=i ω ⇒ω= iz Also arg(z ω)=π ⇒ arg ( iz^2)= π ⇒ arg ( i)+2 arg (z)=π ⇒ π/2+2 arg (z)=π [∵ arg( i)= π/2] ⇒ 2 arg (z)=3 π/2 ⇒ arg (z ...

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Byju's Answer

Standard XIII

Mathematics

Properties of Argument

Let z and ω b...

Question

Let $z$ and $ω$ be complex numbers such that $¯ z + i ¯ ω = 0$ and $a r g z ω = π$ . Then $a r g z$ equals

\frac{π}{4}

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\frac{5 π}{4}

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\frac{3 π}{4}

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\frac{π}{2}

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Solution

The correct option is C $\frac{3 π}{4}$
$¯ z + i ¯ ω = 0 \Rightarrow ¯ z = - i ¯ ω \Rightarrow z = i ω \Rightarrow ω = - i z A l s o a r g (z ω) = π \Rightarrow a r g (- i z^{2}) = π \Rightarrow a r g (- i) + 2 a r g (z) = π \Rightarrow - \frac{π}{2} + 2 a r g (z) = π [∵ a r g (- i) = - \frac{π}{2}] \Rightarrow 2 a r g (z) = \frac{3 π}{2} \Rightarrow a r g (z) = \frac{3 π}{4}$

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Let z and ω be complex numbers such that ¯z+i¯ω=0 and arg zω=π. Then arg z equals

The correct option is C 3π4¯z+i¯ω=0⇒¯z=−i¯ω⇒z=iω⇒ω=−izAlso arg(zω)=π⇒arg(−iz2)=π⇒arg(−i)+2 arg(z)=π⇒−π2+2 arg (z)=π [∵arg(−i)=−π2]⇒2 arg (z)=3π2⇒arg(z)=3π4

Let $z$ and $ω$ be complex numbers such that $¯ z + i ¯ ω = 0$ and $a r g z ω = π$ . Then $a r g z$ equals