Let Z 1 and Z 2 be two complex numbers such that overline z 1= i overline z 2 and arg (( z 1/ overline z 2))=π. Then

Question

Let Z 1 and Z 2 be two complex numbers such that overline z 1= i overline z 2 and arg (( z 1/ overline z 2))=π. Then (A)  arg z 2=(π/4) (B)  arg z 2=-(3 π/4) (C)  arg z 1=(π/4) (D)  arg z 1=-(3 π/4)

Tardigrade Admin · Accepted Answer

overline Z 1= i overline Z 2 z 1=- iz 2 arg (( Z 1/ Z 2))=π arg (- i ( Z 2/ overline Z 2))=π arg ( z 2)=θ -(π/2)+θ+θ=π 2 θ=(3 π/2) arg (z2)=θ=(3 π/4), arg z1=(π/4)

Q. Let $Z_{1}$ and $Z_{2}$ be two complex numbers such that $\overline{z}_{1} = i \overline{z}_{2}$ and $ar g (\frac{z _{1}}{z _{2}}) = π$ . Then

$ar g z_{2} = \frac{π}{4}$

$ar g z_{2} = - \frac{3 π}{4}$

$ar g z_{1} = \frac{π}{4}$

$ar g z_{1} = - \frac{3 π}{4}$

$\overline{Z}_{1} = i \overline{Z}_{2}$
$z_{1} = - i z_{2}$
$ar g (\frac{Z _{1}}{Z _{2}}) = π$
$ar g (- i \frac{Z _{2}}{Z _{2}}) = π$
$ar g (z_{2}) = θ$
$- \frac{π}{2} + θ + θ = π$
$2 θ = \frac{3 π}{2}$
$ar g (z_{2}) = θ = \frac{3 π}{4}, ar g z_{1} = \frac{π}{4}$

Q. Let Z1​ and Z2​ be two complex numbers such that z1​=iz2​ and arg(z2​z1​​)=π. Then

argz2​=4π​

argz2​=−43π​

argz1​=4π​

argz1​=−43π​