Download App

COMPLEX NUMBERS AND QUADRATIC EQUATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS1 Mark
MCQ
If $\sqrt{\text{a}+\text{ib}}=\text{x}+\text{iy},$ then possible value of $\sqrt{\text{a}-\text{ib}}$ is:
  • A
    $\text{x}^2+\text{y}^2$
  • B
    $\sqrt{\text{x}^2+\text{y}^2}$
  • C
    $\text{x}+\text{iy}$
  • ✓
    $\text{x}-\text{iy}$
✓

Answer

Correct option: D.
$\text{x}-\text{iy}$
$\sqrt{\text{a}+\text{ib}}=\text{x}+\text{iy}$
Squaring on both the sides, we get,
$\text{a}+\text{ib}=\text{x}^2+(\text{iy})^2+2\text{ixy}$
$\Rightarrow\text{a}+\text{ib}=(\text{x}^2-\text{y}^2)+2\text{ixy}$
$\therefore\text{a}=(\text{x}^2-\text{y}^2)$
and $\text{b}=2\text{xy}$
$\therefore\text{a}-\text{ib}=(\text{x}^2-\text{y}^2)-2\text{ixy}$
$\Rightarrow\text{a}-\text{ib}=\text{x}^2+\text{i}^2\text{y}^2-2\text{ixy} \ [\because\text{i}^2=-1]$
Taking square root on both the sides, we get:
$\sqrt{\text{a}-\text{ib}}=\text{x}-\text{iy}$

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

More "MCQ" from COMPLEX NUMBERS AND QUADRATIC EQUATIONS→COMPLEX NUMBERS AND QUADRATIC EQUATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following statements is false:
→
The general solution of $sin\, x + sin \,5x = sin\, 2x + sin \,4x$ is :
→
Let $f : (1, 2 ) \to R$ satisfies the inequality $\frac{{\cos (2x - 4)\, - 33}}{2}\,\, < \,\,f(x)\,\, < \,\frac{{{x^2}\,|4x - 8|}}{{x - 2}}$ ,$\forall \,\,x\,\, \in \,(1,2)$ . Then  $\mathop {Lim}\limits_{x \to {2^ - }} \,\,f(x)$ is equal to
→
If $|\text{x}+3|\geq10,$ then:
→
Solving $ – 8 \leq 5\text{x} – 3<7, $ we get:
→
If $x = \frac{{n\pi }}{2}$ , satisfies the equation $sin\, \frac{x}{2}- cos \frac{x}{2} = 1$ $- sin\, x$ & the inequality $\left| {\frac{x}{2}\,\, - \,\,\frac{\pi }{2}} \right|\,\, \le \,\,\frac{{3\pi }}{4}$, then:
→
If the maximum value of $y =\frac{{7\ +\ 6\tan \,x\ -\ {{\tan }^{2\,}}\,x}}{{\left( {1\ +\ {{\tan }^2}\,x} \right)}}$ is $\lambda $ then the value of ${\log _{\sqrt 2 }}\left( \lambda  \right)$ is
→
If $\text{z}=\Big(\frac{1+\text{i}}{1-\text{i}}\Big),$ then $z^4$ equals:
→
The locus of the point of intersection of the lines, $\sqrt 2 x - y + 4\sqrt 2 k = 0$ and $\sqrt 2 kx + ky - 4\sqrt 2  = 0$ ( $k$ is any non-zero real parameter) is
→
The number of ordered pairs $(m, n)$, where $m, n \in\{1,2,3, \ldots, 50\}$, such that $6^m+9^n$ is a multiple of $5$ is
→