Advertisements
Advertisements
प्रश्न
Find a and b if (a + ib) (1 + i) = 2 + i
Advertisements
उत्तर
(a + ib) (1 + i) = 2 + i
∴ a + ai + bi + bi2 = 2 + i
∴ a + (a + b)i + b(–1) = 2 + i …[∵ i2 = – 1]
∴ (a – b) + (a + b)i = 2 + i
Equating real and imaginary parts, we get
a – b = 2 ...(i)
a + b = 1 ...(ii)
Adding equation (i) and (ii), we get
2a = 3
∴ a = `3/2`
Substituting a = `3/2` in (ii),we get
`3/2 +"b"` = 1
∴ b = `1 - 3/2 = -1/2`
a = `3/2`and b = `-1/2`.
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib: i–39
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`
Evaluate the following:
i457
Evaluate the following:
(ii) i528
Find the value of the following expression:
i49 + i68 + i89 + i110
Express the following complex number in the standard form a + i b:
\[\frac{1}{(2 + i )^2}\]
Express the following complex number in the standard form a + i b:
\[\frac{(1 - i )^3}{1 - i^3}\]
Find the real value of x and y, if
\[(x + iy)(2 - 3i) = 4 + i\]
Find the multiplicative inverse of the following complex number:
1 − i
Find the multiplicative inverse of the following complex number:
\[(1 + i\sqrt{3} )^2\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Im `(1/(z_1overlinez_1))`
If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.
Find the real values of θ for which the complex number \[\frac{1 + i cos\theta}{1 - 2i cos\theta}\] is purely real.
Evaluate the following:
\[2 x^4 + 5 x^3 + 7 x^2 - x + 41, \text { when } x = - 2 - \sqrt{3}i\]
If z1 is a complex number other than −1 such that \[\left| z_1 \right| = 1\] and \[z_2 = \frac{z_1 - 1}{z_1 + 1}\] then show that the real parts of z2 is zero.
If \[\left| z + 1 \right| = z + 2\left( 1 + i \right)\],find z.
If z1, z2, z3 are complex numbers such that \[\left| z_1 \right| = \left| z_2 \right| = \left| z_3 \right| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1\] then find the value of \[\left| z_1 + z_2 + z_3 \right|\] .
Write (i25)3 in polar form.
Express the following complex in the form r(cos θ + i sin θ):
tan α − i
Write the value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\] .
Write −1 + i \[\sqrt{3}\] in polar form .
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
If a = cos θ + i sin θ, then \[\frac{1 + a}{1 - a} =\]
The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is
If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =
If \[x + iy = \frac{3 + 5i}{7 - 6i},\] then y =
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i
Find a and b if abi = 3a − b + 12i
Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:
(1 + i)(1 − i)−1
Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:
`((2 + "i"))/((3 - "i")(1 + 2"i"))`
Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:
(1 + i)−3
Show that `(-1 + sqrt(3)"i")^3` is a real number
Evaluate the following : i116
Evaluate the following : i403
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
If z1 and z2 both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.
The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.
