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For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______
For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______
Updated On: Sep 30, 2024
- 3
- $\frac{7}{2}$
- 4
- $\frac{9}{2}$
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The Correct Option is C
Solution and Explanation
\(\sqrt{(3\sqrt2)^2+(p\sqrt2)^2=5\sqrt2 }\)
\(18+2p^2=50 \)
\(p^2=16 \)
\(p=±4\)
The correct option is (C): \(4\)
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Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.
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