Find the greatest and the least value of $| z_{1} + z_{2} |$ if $z_{1} = 24 + 7 i$ and $| z_{2} | = 6.$

least value is 25, greatest value is 31

No worries! We‘ve got your back. Try BYJU‘S free classes today!

least value is 19, greatest value is 31

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

least value is 19, greatest value is 25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

least value is 13, greatest value is 25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B least value is 19, greatest value is 31
$| z_{1} + z_{2} | \leq | z_{1} | + | z_{2} | = | 24 + 7 i | + 6 = 25 + 6 = 31$
Also,
$| z_{1} + z_{2} | = | z_{1} - (- z_{2}) | \geq | | z_{1} | - | z_{2} | | ⟹ | z_{1} + z_{2} | \geq | 25 - 6 | = 19$
Hence, the least value of $| z_{1} + z_{2} |$ is 19 and the greatest value is 31.
Ans: C

Suggest Corrections

Similar questions

| z_{1} + z_{2} |

z_{1} = 24 + 7 i

| z_{2} | = 6

| z_{1} + z_{2} |

z_{1} = 24 + 7 i

| z_{2} | = 6

| z_{1} + z_{2} |

z_{1} = 24 + 7 i a n d | z_{2} | = 6

If |z+7| ≤ 9, for z ∈ C, the greatest value of |Z+2| is __

| $Z_{1}$ + $Z_{2}$ | ≤ | $Z_{1}$ | + | $Z_{2}$ |

| z_{1} - 1 | \leq 1, | z_{2} - 2 | \leq 2, | z_{3} - 3 | \leq 3

| z_{1} + z_{2} + z_{3} |

Join BYJU'S Learning Program