Question

$Z_1=3+4i$ and $|Z_2|=1$. Then, the maximum value of $|Z_1+Z_2|$ is and the minimum value of $|Z_1+Z_2|$ is .

• A. 7
• B. 6
• C. 4
• D. 3

Answer 1

Answer: (B), (C)

The correct options are
B 6
C 4

Given $Z_1=3+4i$ and $|Z_2|=1$

$|Z_1|=\sqrt{3^2+4^2}$
$=\sqrt{25}$
$\Rightarrow |Z_1|=5$

The maximum possible value for $|Z_1+Z_2|$ is $|Z_1|+|Z_2|$, which is 5 + 1, or 6.
The minimum possible value for $|Z_1+Z_2|$ is $||Z_1|-|Z_2||$, which is |5 - 1|, which is 4.