If displaystyle z-1 and displaystyle z-2 are two non-zero complex numbers such that displaystyle -z-1 - z-2- - -z-1- - -z-2- then displaystyle arg z-1 - arg z-2 is equal todisplaystyle - pidisplaystyle pi - 2displaystyle - pi - 20

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Toppr Admin · Accepted Answer

Given-xA0-z1-z2-z1-z2-x21D2-z1-2-z2-2-2Re-z1-xAF-z2-z1-2-z2-2-2-z1-z2-x21D2-Re-z1-xAF-z2-z1-z2-x21D2-Re-z1-xAF-z2-z1-xAF-z2-or-xA0-Re-xAF-z1z2-xAF-z1z2-x21D2-z1-xAF-z2-R-x21D2-Arg-z1-xAF-z2-Arg-xAF-z1z2-0-x21D2-Argz1-Arg-xAF-z2-Arg-xAF-z1-Argz2-0-x21D2-Argz1-x2212-Argz2-x2212-Argz1-Argz2-0

If z1 and z2 are two non-zero complex numbers such that |z1+z2|=|z1|+|z2|, then argz1−argz2 is equal to−ππ/2−π/20

Given z1+z2|=|z1|+|z2|⇒|z1|2+|z2|2+2Re(z1¯z2)=|z1|2+|z2|2+2|z1||z2|⇒Re(z1¯z2)=|z1||z2|⇒Re(z1¯z2)=|z1¯z2|(or Re(¯z1z2)=|¯z1z2|)⇒z1¯z2=R+⇒Arg(z1¯z2)=Arg(¯z1z2)=0⇒Argz1+Arg¯z2=Arg¯z1+Argz2=0⇒Argz1−Argz2=−Argz1+Argz2=0

If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $| z_{1} + z_{2} | = | z_{1} | + | z_{2} |$ , then $a r g z_{1} - a r g z_{2}$ is equal to
$- π$
$π / 2$
$- π / 2$
0