Advertisements
Advertisements
प्रश्न
sinx + icos2x and cosx – isin2x are conjugate to each other for ______.
पर्याय
x = nπ
x = `(n + 1/2) pi/2`
x = 0
No value of x
Advertisements
उत्तर
sinx + icos2x and cosx – isin2x are conjugate to each other for x = 0.
Explanation:
Let z = sinx + icos2x
`barz` = sinx – icos2x
But we are given that `barz` = cosx – isin2x
∴ sinx – icos2x = cosx – isin2x
Comparing the real and imaginary parts, we get
sinx = cosx and cos2x = sin2x
⇒ tanx = 1 and tan2x = 1
⇒ tanx = `tan pi/4` and tan2x = `pi/4`
∴ x = `npi + pi/4`, n ∈ I and 2x = `npi + pi/4`
⇒ x = 2x
⇒ 2x – x = 0
⇒ x = 0
APPEARS IN
संबंधित प्रश्न
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.
Find the modulus of `(1+i)/(1-i) - (1-i)/(1+i)`
Find the conjugate of the following complex number:
4 − 5 i
Find the conjugate of the following complex number:
\[\frac{1}{3 + 5i}\]
Find the conjugate of the following complex number:
\[\frac{(3 - i )^2}{2 + i}\]
Find the conjugate of the following complex number:
\[\frac{(3 - 2i)(2 + 3i)}{(1 + 2i)(2 - i)}\]
Find the modulus of \[\frac{1 + i}{1 - i} - \frac{1 - i}{1 + i}\].
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\sqrt{3} + i\]
Find the modulus and argument of the following complex number and hence express in the polar form:
1 − i
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1 - i}{1 + i}\]
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1}{1 + i}\]
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1 + 2i}{1 - 3i}\]
Find the modulus and argument of the following complex number and hence express in the polar form:
sin 120° - i cos 120°
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{- 16}{1 + i\sqrt{3}}\]
If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, prove that \[\arg\left( \frac{z_1}{z_4} \right) + \arg\left( \frac{z_2}{z_3} \right) = 0\].
If (1 + i) (1 + 2i) (1 + 3i) .... (1 + ni) = a + ib, then 2.5.10.17.......(1+n2)=
If \[x + iy = (1 + i)(1 + 2i)(1 + 3i)\],then x2 + y2 =
Solve the equation `z^2 = barz`, where z = x + iy.
If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (–4, 0), find the greatest and least values of |z + 1|.
The conjugate of the complex number `(1 - i)/(1 + i)` is ______.
If a complex number lies in the third quadrant, then its conjugate lies in the ______.
If z1 = `sqrt(3) + i sqrt(3)` and z2 = `sqrt(3) + i`, then find the quadrant in which `(z_1/z_2)` lies.
What is the conjugate of `(sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) - sqrt(5 - 12i))`?
If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then find arg`(z_1/z_4)` + arg`(z_2/z_3)`.
Solve the system of equations Re(z2) = 0, z = 2.
If z = x + iy lies in the third quadrant, then `barz/z` also lies in the third quadrant if ______.
