1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider the following statements. I. Let z1 and z2 be two complex numbers such that |z1+z2|=|z1|+|z2| then arg (z1)- arg (z2)=0 II. Roots of quadratic equation x2+3 x+5=0 is x=(-3 ± i √11/2) Choose the correct option

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Q. Consider the following statements.
$I$. Let $z_{1}$ and $z_{2}$ be two complex numbers such that $\left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right|$ then $\arg \left(z_{1}\right)-\arg \left(z_{2}\right)=0$
$II$. Roots of quadratic equation
$x^{2}+3 x+5=0$ is $x=\frac{-3 \pm i \sqrt{11}}{2}$
Choose the correct option

Complex Numbers and Quadratic Equations

Solution:

II. $x^{2}+3 x+5=0$
$x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)}}{2}=\frac{-3 \pm \sqrt{9-20}}{2}$
$=\frac{-3 \pm \sqrt{11} i}{2}$