Download App

4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $(a + ib)(c + id)(e + if)(g + ih)$$ = A + iB,$ then $({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2})$ =
  • ✓
    ${A^2} + {B^2}$
  • B
    ${A^2} - {B^2}$
  • C
    ${A^2}$
  • D
    ${B^2}$
✓

Answer

Correct option: A.
${A^2} + {B^2}$
a
(a)$(a + ib)(c + id)(e + if)(g + ih) = A + iB$.....$(i)$
==> $(a - ib)(c - id)(e - if)(g - ih) = A - iB$......$(ii)$
Multiplying $(i) $ and $(ii)$, we get
$({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2}) = {A^2} + {B^2}$
 

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 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer. $x-$axis is the intersection of two planes:
→
If $n(U)$ = $600$ , $n(A)$ = $100$ , $n(B)$ = $200$ and $n(A \cap  B )$ = $50$, then $n(\bar A  \cap \bar B )$ is 

($U$ is universal set and $A$ and $B$ are subsets of $U$)

→
The median of $100$ observations grouped in classes of equal width is $25.$ If the median class interval is $20 - 30$ and the number of observations less than $20$ is $4 5,$ then the frequency of median class is
→
Let $A_1, A_2, A_3, \ldots \ldots ., A_8$ be the vertices of a regular octagon that lie on a circle of radius $2$ . Let $P$ be a point on the circle and let $\mathrm{PA}_{\mathrm{i}}$ denote the distance between the points $P$ and $\mathrm{A}_{\mathrm{i}}$ for $i=1,2, \ldots, 8$. If $P$ varies over the circle, then the maximum value of the product $\mathrm{PA}_1 \cdot \mathrm{PA}_2 . \cdots \cdot \mathrm{PA}_8$, is
→
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
→
In an examination, 34% of the candidates fail in Arithmetic and 42% in English.If 20% fail in Arithmetic and English, the percentage of those passing in both subjects is:
→
If the point dividing internally the line segment joining the points $(a, b)$ and $(5, 7)$ in the ratio $2 : 1$ be $(4, 6)$, then
→
If $3 x+4 y=12 \sqrt{2}$ is a tangent to the ellipse $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{9}=1$ for some a $\in \mathrm{R},$ then the distance between the foci of the ellipse is
→
If $\omega $ is an $n^{th}$ root of unity, other than unity, then the value of $1 + \omega + {\omega ^2} + ... + {\omega ^{n - 1}}$ is
→
The equation of the circle whose diameters have the end points $(a, 0), (0, b)$ is given by
→