Advertisements
Advertisements
प्रश्न
Find the real value of x and y, if
\[(x + iy)(2 - 3i) = 4 + i\]
Advertisements
उत्तर
\[ \left( x + iy \right)\left( 2 - 3i \right) = 4 + i\]
\[2x - 3ix + 2iy - 3 i^2 y = 4 + i\]
\[2x + 3y + i\left( - 3x + 2y \right) = 4 + i\]
\[\text{Comparing both the sides:} \]
\[2x + 3y = 4 . . . . (1) \]
\[ - 3x + 2y = 1 . . . . (2)\]
\[\text { Multiplying equation (1) by 3 and equation (2) by 2 }: \]
\[ 6x + 9y = 12 . . . (3)\]
\[ - 6x + 4y = 2 . . . (4)\]
\[\text { Adding equations (3) and (4) }: \]
\[13y = 14\]
\[y = \frac{14}{13}\]
\[\text { Substituting the value of y in equation (1):} \]
\[2x + 3 \times \frac{14}{13} = 4\]
\[ \Rightarrow 2x = 4 - \frac{42}{13}\]
\[ \Rightarrow 2x = \frac{10}{13}\]
\[ \Rightarrow x = \frac{5}{13}\]
\[ \therefore x = \frac{5}{13}\text { and } y = \frac{14}{13} \]
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
Express the given complex number in the form a + ib: `(1/3 + 3i)^3`
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Evaluate the following:
(ii) i528
Evaluate the following:
\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of the following expression:
\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]
Find the value of the following expression:
1+ i2 + i4 + i6 + i8 + ... + i20
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:
\[\frac{(1 - i )^3}{1 - i^3}\]
Find the real value of x and y, if
\[(3x - 2iy)(2 + i )^2 = 10(1 + i)\]
Find the multiplicative inverse of the following complex number:
\[(1 + i\sqrt{3} )^2\]
If \[\left( \frac{1 + i}{1 - i} \right)^3 - \left( \frac{1 - i}{1 + i} \right)^3 = x + iy\] find (x, y).
If \[\left( \frac{1 - i}{1 + i} \right)^{100} = a + ib\] find (a, b).
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.
Find the number of solutions of \[z^2 + \left| z \right|^2 = 0\].
Express the following complex in the form r(cos θ + i sin θ):
1 + i tan α
If π < θ < 2π and z = 1 + cos θ + i sin θ, then write the value of \[\left| z \right|\] .
Find the principal argument of \[\left( 1 + i\sqrt{3} \right)^2\] .
Write the value of \[\sqrt{- 25} \times \sqrt{- 9}\].
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]
The argument of \[\frac{1 - i}{1 + i}\] is
The value of (i5 + i6 + i7 + i8 + i9) / (1 + i) is
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
Which of the following is correct for any two complex numbers z1 and z2?
If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on
Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`
Find a and b if (a – b) + (a + b)i = a + 5i
Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:
`("i"(4 + 3"i"))/((1 - "i"))`
Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:
`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"i")`
Express the following in the form of a + ib, a, b ∈ R i = `sqrt(−1)`. State the values of a and b:
`(2 + sqrt(-3))/(4 + sqrt(-3))`
Express the following in the form of a + ib, a, b ∈ R i = `sqrt(−1)`. State the values of a and b:
`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`
Show that `(-1 + sqrt(3)"i")^3` is a real number
Evaluate the following : i888
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
