Advertisements
Advertisements
प्रश्न
Find the real value of x and y, if
\[(1 + i)(x + iy) = 2 - 5i\]
Advertisements
उत्तर
\[ \left( 1 + i \right)\left( x + iy \right) = 2 - 5i\]
\[ \Rightarrow x + iy + ix + i^2 y = 2 - 5i\]
\[ \Rightarrow x + iy + ix - y = 2 - 5i\]
\[ \Rightarrow \left( x - y \right) + i\left( y + x \right) = 2 - 5i\]
\[\text { Comparing both the sides }, \]
\[x - y = 2 . . . (1) \]
\[x + y = - 5 . . . (2)\]
\[\text { Adding equations (1) and (2) }, \]
\[2x = - 3\]
\[ \Rightarrow x = \frac{- 3}{2}\]
\[\text { Substituting the value of x in equation (1) }, \]
\[\frac{- 3}{2} - y = 2\]
\[ \Rightarrow y = \frac{- 3}{2} - 2\]
\[ \Rightarrow y = \frac{- 7}{2}\]
\[ \therefore x = \frac{- 3}{2} \text { and y } = \frac{- 7}{2}\]
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: `(1/5 + i 2/5) - (4 + i 5/2)`
Express the given complex number in the form a + ib: (1 – i)4
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:
\[i^{30} + i^{40} + i^{60}\]
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:
\[\frac{1}{(2 + i )^2}\]
Express the following complex number in the standard form a + i b:
\[(1 + i)(1 + 2i)\]
Express the following complex number in the standard form a + i b:
\[\left( \frac{1}{1 - 4i} - \frac{2}{1 + i} \right)\left( \frac{3 - 4i}{5 + i} \right)\]
Express the following complex number in the standard form a + i b:
\[\frac{5 + \sqrt{2}i}{1 - 2\sqrt{i}}\]
Find the least positive integral value of n for which \[\left( \frac{1 + i}{1 - i} \right)^n\] is real.
Evaluate the following:
\[x^6 + x^4 + x^2 + 1, \text { when }x = \frac{1 + i}{\sqrt{2}}\]
Evaluate the following:
\[2 x^4 + 5 x^3 + 7 x^2 - x + 41, \text { when } x = - 2 - \sqrt{3}i\]
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
Express the following complex in the form r(cos θ + i sin θ):
tan α − i
If z1 and z2 are two complex numbers such that \[\left| z_1 \right| = \left| z_2 \right|\] and arg(z1) + arg(z2) = \[\pi\] then show that \[z_1 = - \bar{{z_2}}\].
If n is any positive integer, write the value of \[\frac{i^{4n + 1} - i^{4n - 1}}{2}\].
If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.
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 \[\left| a z_1 - b z_2 \right|^2 + \left| a z_2 + b z_1 \right|^2\].
If \[z = \frac{- 2}{1 + i\sqrt{3}}\],then the value of arg (z) is
If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to
If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]
\[(\sqrt{- 2})(\sqrt{- 3})\] is equal to
The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is
\[\text { If } z = \frac{1}{(1 - i)(2 + 3i)}, \text { than } \left| z \right| =\]
If \[z = \frac{1 + 7i}{(2 - i )^2}\] , then
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
Simplify : `4sqrt(-4) + 5sqrt(-9) - 3sqrt(-16)`
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:
(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 + 3i)(2 – 3i)
Show that `(-1 + sqrt3 "i")^3` is a real number.
If w is a complex cube-root of unity, then prove the following
(w2 + w − 1)3 = −8
