If 1-ix 1+ix =a+ib, then a^2+b^2= - Vidyadip

MCQ

If $\frac{1-\text{ix}}{1+\text{ix}}=\text{a}+\text{ib},$ then $\text{a}^2+\text{b}^2=$

A
1
B
-1
C
0
D
none of these

✓

Answer

1

Solution:

$\frac{1-\text{ix}}{1+\text{ix}}=\text{a}+\text{ib}$

Taking modulus on both the sides, we get:

$\Big|\frac{1-\text{ix}}{1+\text{ix}}\Big|=\big|\text{a}+\text{ib}\big|$

$\Rightarrow\frac{\sqrt{1^2+\text{x}^2}}{\sqrt{1^2+\text{x}^2}}=\sqrt{\text{a}^2+\text{b}^2}$

$\Rightarrow\sqrt{\text{a}^2+\text{b}^2}=1$

Squaring both the sides, we get:

$\text{a}^2+\text{b}^2=1$

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 z₁ and z₂ be two com plex num bers with α and$\beta$ as their prin ci pal ar gu ments such that $\alpha+\beta>\pi,$ then prin ci pal arg (z₁z₂) is given by:

If the circle x² + y² = 9 passesthrough (2, c) then c is equal to:

The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is.

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is:

If n is a positive integer, then $\Big(\frac{1+\text{i}}{1-\text{i}}\Big)4\text{n}+1$ is equal to:

If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3 $\text{P(A)}=2\text{P(B)}=\text{C},$ then P(A) is equal to:

$\frac{1}{11}$
$\frac{2}{11}$
$\frac{5}{11}$
$\frac{6}{11}$

If $A + B + C =\frac{\pi}{2}$, then the value of $\sin ( A + B )$ is :

For a frequency distribution mean deviation from mean is computed by:

$\text{M.D.}=\frac{\sum\text{f}}{\sum\text{f}\ |\text{d}|}$
$\text{M.D.}=\frac{\sum\text{d}}{\sum\text{f}}$
$\text{M.D.}=\frac{\sum\text{fd}}{\sum\text{f}}$
$\text{M.D.}=\frac{\sum\text{f}\ |\text{d}|}{\sum\text{f}}$

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:

s
ks
s + k
$\frac{\text{s}}{\text{k}}$

If the zx-plane divides the line segment joining (1, -1, 5) and (2, 3, 4) in the ratio p : 1 then p + 1 =