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
Evaluate: `[i^18 + (1/i)^25]^3`
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
Evaluate the following:
\[\frac{1}{i^{58}}\]
Evaluate the following:
\[i^{37} + \frac{1}{i^{67}}\].
Evaluate the following:
\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of the following expression:
i49 + i68 + i89 + i110
Find the value of the following expression:
i + i2 + i3 + i4
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:
\[\frac{2 + 3i}{4 + 5i}\]
Find the multiplicative inverse of the following complex number:
1 − i
If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.
If \[\left( \frac{1 + i}{1 - i} \right)^3 - \left( \frac{1 - i}{1 + i} \right)^3 = x + iy\] find (x, y).
If \[a = \cos\theta + i\sin\theta\], find the value of \[\frac{1 + a}{1 - a}\].
If π < θ < 2π and z = 1 + cos θ + i sin θ, then write the value of \[\left| z \right|\] .
The value of \[(1 + i)(1 + i^2 )(1 + i^3 )(1 + i^4 )\] is.
If i2 = −1, then the sum i + i2 + i3 +... upto 1000 terms is equal to
The principal value of the amplitude of (1 + i) is
\[(\sqrt{- 2})(\sqrt{- 3})\] is equal to
If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals
\[\text { If } z = \frac{1}{(1 - i)(2 + 3i)}, \text { than } \left| z \right| =\]
\[\text { If }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]
If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =
\[\frac{1 + 2i + 3 i^2}{1 - 2i + 3 i^2}\] equals
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
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
A real value of x satisfies the equation \[\frac{3 - 4ix}{3 + 4ix} = a - ib (a, b \in \mathbb{R}), if a^2 + b^2 =\]
If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on
Find a and b if `1/("a" + "ib")` = 3 – 2i
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)
Evaluate the following : i888
Evaluate the following : i116
Evaluate the following : i–888
Show that 1 + i10 + i20 + i30 is a real number
State true or false for the following:
If a complex number coincides with its conjugate, then the number must lie on imaginary axis.
