Download App

Complex Numbers and Quadratic Equations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations1 Mark
MCQ
If z = 3 + 5i, then z3 + z + 198 =
  • A
    3 - 15i
  • B
    -3 - 15i
  • C
    -3 + 15i
  • D
    3 + 15i
✓

Answer

  1. 3 + 15i

Solutions:

 

z = 3 + 5i

z3 = (3 + 5i)3

= 33 + 3.32(5i) + 3.3(5i)2 + (5i)3

= 27 - 125i + 135i - 225

= -225 + 27 + (135 - 125)i

= -198 + 10i

$\therefore$ z3 + z + 198

= -198 + 10i + 3 + 5i + 198

= 3 + 15i

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 "M.C.Q (1 Marks)" from Complex Numbers and Quadratic Equations→Complex Numbers and Quadratic Equations — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let A and B be finite sets containing m and n elements respectively. The number of relations that can be defined from A to B is
→
In any $\triangle\text{ABC},\sum\text{a}^2(\sin\text{B}-\sin\text{C})=$
  1. $\text{a}^2+\text{b}^2+\text{c}^2$
  2. $\text{a}^2$
  3. $\text{b}^2$
  4. $0$
→

If 4-digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5 and 7, then the probability of forming a number divisible by 5 when the digits are repeated is:

→
The number of permutations of n different things taking r at a time when 3 particular things are to be included is:
→

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is:

  1. s
  2. ks
  3. s + k
  4. $\frac{\text{s}}{\text{k}}$
→
What is the number of critical points of $\text{f}(\text{x}) = \frac{|\text{x}^2 - 1|}{ \text{x}^2} ?$
→
If line passing through point $(4,3)$ and $(2, k)$ is perpendicular to the line $y=2 x+3$, then $k$ equals to :
→
Centre of the circle $x^2+y^2-10 x+16 y+6=0$ is at :
→
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is:
  1. 216
  2. 600
  3. 240
  4. 3125
→
The mean of x, x + 3, x + 4, x + 8 and x + 10:
→