Let z - w be complex numbers such that z - i w -0 and argzw- Then z equalsA- 5 -4-B- 2-2C- 3 -4D- -4

Given that arg zw = π .......... (i) z̅+i̅w̅=0 ⇒z̅= i̅w̅⇒ z=iw ⇒ w= iz From (i), arg ( iz^2)= π arg ( i)+2 arg (z)= π; π/2+ 2 arg(z)=π 2 arg(z)=3π/2; arg ...

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Byju's Answer

Standard XII

Mathematics

Properties of Argument

Let z , w be ...

Question

Let z, w be complex numbers such that $¯ z + ¯ i w = 0 a n d a r g z w = π$ . Then arg z equals

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Solution

The correct option is C
Given that arg zw = $π$ .......... (i)
$¯ z + ¯ i w = 0 \Rightarrow ¯ z = - ¯ i w \Rightarrow z = i w \Rightarrow w = - i z F r o m (i), a r g (- i z^{2}) = π a r g (- i) + 2 a r g (z) = π; \frac{- π}{2} + 2 a r g (z) = π 2 a r g (z) = \frac{3 π}{2}; a r g (z) = \frac{3 π}{4}$

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The correct option is C Given that arg zw = π .......... (i) ¯z+¯iw=0⇒¯z=−¯iw⇒z=iw⇒w=−izFrom(i), arg (−iz2)=πarg(−i)+2arg(z)=π;−π2+2 arg(z)=π2arg(z)=3π2; arg(z)=3π4

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