Question

P and q are complex numbers such that |p|=7√2 and |p+q|=12√3 .

On what interval must |q| fall on?



A [7√6/24,[infinity])



B [12√3−7√2,[infinity])



C [12√3+7√2,[infinity])



D [4√6/7,[infinity])

Answer 1

Option B is correct

Explanation:

Given:
`\left | p \right |=7√(2)\,,\,\left | p+q \right |=12√(3)`

To find: interval on which
`\left | q \right |` must fall

Solution:

`\left | p \right |=7√(2)\\-7√(2)\leq p\leq 7√(2)\,\,(i)`

`\left | p+q \right |=12√(3)\\-12√(3)\leq p+q\leq 12√(3)\,\,(ii)`

Subtract (ii) from (i)

`-12√(3)+7√(2)\leq p+q-p\leq 12√(3)-7√(2)\\-12√(3)+7√(2)\leq q\leq 12√(3)-7√(2)\\\left | q \right |=12√(3)-7√(2)`

So,
`\left | q \right |` must fall in interval
`[12√(3)-7√(2),\infty)`

Therefore, option B is correct.