For a complex number Z, if Z-i≤2 and Z_1=5+3i, then the maximum value of iZ+Z_1 is (where, i^2=-1)

Correct answer: (C) 7. iZ+Z_1=iZ-i+Z_1-1 ≤iZ-i+Z_1-1 ≤iZ-i+4+3i ≤2+√(4^2+3^2)=7

Q46 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Complex Number

For a complex number $Z$ , if $|Z - i| \leq 2$ and $Z_{1} = 5 + 3 i$ , then the maximum value of $|i Z + Z_{1}|$ is (where, $i^{2} = - 1$ )

|i Z + Z_{1}| = |i (Z - i) + (Z_{1} - 1)|

\leq |i (Z - i)| + |Z_{1} - 1|

\leq |i| |Z - i| + |4 + 3 i|

\leq 2 + \sqrt{4^{2} + 3^{2}} = 7

Hence, the correct answer is option: 'C'.