Let z1 and z2 are two complex numbers such that |z1|=|z2| and arg(z1)+arg(z2)=π , then z1 equals to

Question

Let z1 and z2 are two complex numbers such that |z1|=|z2| and arg(z1)+arg(z2)=π , then z1 equals to (A) z2 (B) -z2 (C)  overlinez2 (D) - overlinez2

Tardigrade Admin · Accepted Answer

We have given that, |z1|=|z2| and arg(z1)=π -arg(z2) z2=rei θ , barz2=re- i θ z1=rei (. π - θ .)=rei π ⋅ e- i θ =r(.cosπ +isinπ .)⋅ e- i θ =-re- i θ =- overlinez2 Alternate Solution <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-uoxhqlnbzsaazxyy.jpg" /> From figure, it is clear that z1=- barz2

Q. Let $z_{1}$ and $z_{2}$ are two complex numbers such that $∣ z_{1} ∣ = ∣ z_{2} ∣$ and $a r g (z_{1}) + a r g (z_{2}) = π$ , then $z_{1}$ equals to

$z_{2}$

$- z_{2}$

$\overline{z}_{2}$

$- \overline{z}_{2}$

Q. Let z1​ and z2​ are two complex numbers such that ∣z1​∣=∣z2​∣ and arg(z1​)+arg(z2​)=π , then z1​ equals to

z2​

−z2​

z2​