Let complex number z be such that |z - frac{6 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $|z - \frac{6}{z}| = 5$. Using the triangle inequality property $||z_1| - |z_2|| \leq |z_1 - z_2|$,we have $|z| - |\frac{6}{z}| \leq |z - \f

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) Given $|z - \frac{6}{z}| = 5$. Using the triangle inequality property $||z_1| - |z_2|| \leq |z_1 - z_2|$,we have $|z| - |\frac{6}{z}| \leq |z - \frac{6}{z}|$. Substituting the given value: $|z| - \frac{6}{|z|} \leq 5$. Let $|z| = r$,where $r > 0$. Then $r - \frac{6}{r} \leq 5$. Multiplying by $r$ (since $r > 0$): $r^2 - 6 \leq 5r \Rightarrow r^2 - 5r - 6 \leq 0$. Factoring the quadratic: $(r - 6)(r + 1) \leq 0$. Since $r > 0$,we must have $r \leq 6$. Thus,the maximum value of $|z|$ is $6$.

Let complex number $z$ be such that $|z - \frac{6}{z}| = 5$,then the maximum value of $|z|$ will be -

Similar Questions

If $|z_1| = |z_2|$ and $\text{amp}(z_1) + \text{amp}(z_2) = 0$,then

The product of two complex numbers,each of unit modulus,is also a complex number of:

If $ \alpha $ and $ \beta $ are two different complex numbers with $ |\beta|=1 $,then $ \left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right| $ is equal to

If $z_1=1-2 i, z_2=1+i$ and $z_3=3+4 i$,then $\left|\left(\frac{1}{z_1}+\frac{2}{z_2}\right) \frac{z_3}{z_2}\right|=$

Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module