Download App

4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $z = 3 + 5i,\,\,{\rm{then }}\,{z^3} + \bar z + 198 = $
  • A
    $ - 3 - 5i$
  • B
    $ - 3 + 5i$
  • ✓
    $3 + 5i$
  • D
    $3 - 5i$
✓

Answer

Correct option: C.
$3 + 5i$
c
(c) $z = 3 + 5i$, $\bar z = 3 - 5i$
$ \Rightarrow \,$${z^3} = {(3 + 5i)^3} = {3^3} + {(5i)^3} + 3.3.5i\,(3 + 5i)$
$ = - 198 + 10i$
Hence, ${z^3} + \bar z + 198 = 10\,i - 198 + 3 - 5\,i + 198 = 3 + 5\,i$.
 

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

The first term of a $G.P.$ is $7$, the last term is $448$ and sum of all terms is $889$, then the common ratio is
→
For all n∈N, 72n − 48n−1 is divisible by:
→
How many rational and irrational numbers are possible between 0 and 1?
→
The equation of circle described on the chord $3x + y+ 5\, = 0$ of the circle $x^2 + y^2\, = 16$ as diameter is
→
The number of ways in which $6$ rings can be worn on the four fingers of one hand is
→
If each term of a geometric progression $a_1, a_2, a_3, \ldots$ with $a_1=\frac{1}{8}$ and $a_2 \neq a_1$, is the arithmetic mean of the next two terms and $S_n=a_1+a_2+\ldots+a_n$, then $\mathrm{S}_{20}-\mathrm{S}_{18}$ is equal to
→
For all $n \geq 2, n n^2\left(n^4>1\right)$ is divisible by:
→
If in an examination different weights are assigned to different subjects. Physics $(2)$, Chemistry $(1)$, English $(1) $ Mathematics $(2)$. If a student scored $60$ in Physics, $70$ in Chemistry, $70$ in English and $80$ in Mathematics, then his weighted $A.M.$ is :-
→
In a game, a man wins $Rs.\,100$  if he gets $5$ or $6$ on a throw of a fair die and loses $Rs.\,50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is
→
For all $10^n+3\left(4^{n+2}\right)+5$ is divisible by $(n \in N)$ :
→