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

Question

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 (A) Only I is correct. (B) Only II is correct. (C) Both are correct. (D) Neither I nor II is correct.

Tardigrade Admin · Accepted Answer

II. x2+3 x+5=0 x=(-3 ± √(3)2-4(5)/2)=(-3 ± √9-20/2) =(-3 ± √11 i/2)

Q. 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+3x+5=0 is x=2−3±i11​​ Choose the correct option

Only I is correct.

Only II is correct.

Both are correct.

Neither I nor II is correct.

II. x2+3x+5=0 x=2−3±(3)2−4(5)​​=2−3±9−20​​ =2−3±11​i​

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