Question

If $|z|<4$, then $|iz+3-4i|$ is less then

• A. $4$
• B. $5$
• C. $9$
• D. $6$

Answer 1

The correct option is C $9$

Given, $|z|<4$......(1).

Now

$|iz+3-4i|$$\le |iz|+|(3-4i)|$ [ Using standard inequility of sum of two complex number]

or, $|iz+3-4i|$$\le |z|+5$ [ Since $|iz|=|z|$]

or, $|iz+3-4i|$$<4+5$ [ Using (1)]

or, $|iz+3-4i|$$<9$.