The greatest and the least value of |z1 + z2| if z1 =24+7i and |z2|=6 respectively are

Question

The greatest and the least value of |z1 + z2| if z1 =24+7i and |z2|=6 respectively are (A) 31,19 (B) 19,25 (C) -19,-25 (D) -25,-19

Tardigrade Admin · Accepted Answer

z1+z2 ≤ z1+z2=|24+7 i|+6=25+6=31 Also, z1+z2=z1--z2 ≥ | z1|-| z2|| ⇒ z1+z2 ≥|25-6|=19 Hence the least value of z1+z2 is 19 and the greatest value is 31 .

Q. The greatest and the least value of $∣ z_{1} + z_{2} ∣$ if $z_{1}$ $= 24 + 7 i$ and $∣ z_{2} ∣ = 6$ respectively are

$31, 19$

$19, 25$

$- 19, - 25$

$- 25, - 19$

$z_{1} + z_{2} \leq z_{1} + z_{2} = ∣24 + 7 i ∣ + 6 = 25 + 6 = 31$
Also, $z_{1} + z_{2} = z_{1} - - z_{2} \geq ∥ z_{1} ∣ - ∣ z_{2} ∣∣$
$\Rightarrow z_{1} + z_{2} \geq ∣25 - 6∣ = 19$
Hence the least value of $z_{1} + z_{2}$ is $19$ and the greatest value is $31$ .

Q. The greatest and the least value of ∣z1​+z2​∣ if z1​ =24+7i and ∣z2​∣=6 respectively are

31,19

19,25

−19,−25

−25,−19