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: `(5i) (- 3/5 i)`
Express the given complex number in the form a + ib: i9 + i19
Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)
Express the given complex number in the form a + ib:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Evaluate the following:
\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]
Find the value of the following expression:
i5 + i10 + i15
Find the value of the following expression:
\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]
Express the following complex number in the standard form a + i b:
\[\frac{1 - i}{1 + i}\]
Express the following complex number in the standard form a + i b:
\[\frac{2 + 3i}{4 + 5i}\]
Express the following complex number in the standard form a + i b:
\[\frac{5 + \sqrt{2}i}{1 - 2\sqrt{i}}\]
Evaluate the following:
\[x^6 + x^4 + x^2 + 1, \text { when }x = \frac{1 + i}{\sqrt{2}}\]
If \[\left| z + 1 \right| = z + 2\left( 1 + i \right)\],find z.
Express the following complex in the form r(cos θ + i sin θ):
1 + i tan α
Write 1 − i in polar form.
If \[\frac{\left( a^2 + 1 \right)^2}{2a - i} = x + iy\] find the value of \[x^2 + y^2\].
For any two complex numbers z1 and z2 and any two real numbers a, b, find the value of \[\left| a z_1 - b z_2 \right|^2 + \left| a z_2 + b z_1 \right|^2\].
The value of \[(1 + i)(1 + i^2 )(1 + i^3 )(1 + i^4 )\] is.
If\[z = \cos\frac{\pi}{4} + i \sin\frac{\pi}{6}\], then
If i2 = −1, then the sum i + i2 + i3 +... upto 1000 terms is equal to
If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals
If \[z = \frac{1 + 2i}{1 - (1 - i )^2}\], then arg (z) equal
The argument of \[\frac{1 - i}{1 + i}\] is
The value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1\] is
Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i
Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:
(1 + 2i)(– 2 + i)
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
Find the value of `(3 + 2/i) (i^6 - i^7) (1 + i^11)`.
Evaluate the following : i35
Evaluate the following : i–888
Evaluate the following : i30 + i40 + i50 + i60
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
If a = cosθ + isinθ, find the value of `(1 + "a")/(1 - "a")`.
State True or False for the following:
2 is not a complex number.
Show that `(-1 + sqrt3 "i")^3` is a real number.
