Download App

STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
Question
A function $f$ is defined on the complex number by $f(z) = (a + ib)z$ , where $a,b \in {\mathbb{R}^ + }$ .This function has the property that the $f-$ image of any point in the complex plane is equidistant from that point and origin. If $|a + bi|= 10$ and ${b^2} = \frac{p}{q}\,;\,p,q \in \mathbb{Z}$ , $gcd(p, q) = 1$ , then $p + q$ is
✓

Answer

b
$|(a+i b) z-z|=|(a+i b) z|$

$|z||a-1+i b|=|z||a+i b|$

$\Rightarrow \quad a=\frac{1}{2}$

Now $a^{2}+b^{2}=100$

$\Rightarrow \quad b^{2}=\frac{399}{4}$

$\Rightarrow p+q=399+4=403$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$tan^{-1} \frac{x}{\pi} < \frac{\pi}{3} ,x \in N,$ then the maximum value of $x$ is :-
→
If sum of two numbers is $3$, then maximum value of the product of first and the square of second is
→
The mean and standard deviation of $10$ observations are $20$ and $84$ respectively. Later on, it was observed that one observation was recorded as $50$ instead of $40$. Then the correct variance is:
→
If $\frac{{c + i}}{{c - i}} = a + ib$, where $a,b,c$are real, then ${a^2} + {b^2} = $
→
The area enclosed by the graphs of $|x + y| = 2$ and $|x| = 1$ is
→
Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in R$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to -
→
The total number of $3 \times 3$ matrices $A$ having enteries from the set $(0,1,2,3)$ such that the sum of all the diagonal entries of $AA ^{ T }$ is $9$, is equal to........
→
A tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}}$ + $\frac{{{y^2}}}{{32}}$ $= 1$  intersects the major and minor axes in points $A$ and $ B$  respectively. If $C$  is the centre of the ellipse then the area of the triangle $ ABC$  is : .............. $\mathrm{sq. \,units}$
→
Let $f$ be a differentiable function in the interval $(0, \infty)$ such that $f(1)=1$ and $\lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1$ for each $x>0$. Then $2 f(2)+3 f(3)$ is equal to ....................
→
The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
→