Advertisements
Advertisements
प्रश्न
Find a and b if (a – b) + (a + b)i = a + 5i
Advertisements
उत्तर
(a – b) + (a + b)i = a + 5i
Equating the real and imaginary parts separately, we get,
a – b = a ...(1)
and a + b = 5 ...(2)
From (1), – b = 0
∴ b = 0
∴ from (2), a + 0 = 5
∴ a = 5
Hence, a = 5, b = 0.
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:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
Evaluate the following:
i457
Evaluate the following:
\[\frac{1}{i^{58}}\]
Evaluate the following:
\[i^{37} + \frac{1}{i^{67}}\].
Evaluate the following:
\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]
Find the value of the following expression:
i + i2 + i3 + i4
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:
\[\frac{1}{(2 + i )^2}\]
Express the following complex number in the standard form a + i b:
\[(1 + i)(1 + 2i)\]
Find the multiplicative inverse of the following complex number:
\[(1 + i\sqrt{3} )^2\]
If \[z_1 = 2 - i, z_2 = 1 + i,\text { find } \left| \frac{z_1 + z_2 + 1}{z_1 - z_2 + i} \right|\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Re \[\left( \frac{z_1 z_2}{z_1} \right)\]
Evaluate the following:
\[x^6 + x^4 + x^2 + 1, \text { when }x = \frac{1 + i}{\sqrt{2}}\]
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 \[\left| z_1 + z_2 + z_3 \right|\] .
If \[\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}\],find z.
The value of \[(1 + i)(1 + i^2 )(1 + i^3 )(1 + i^4 )\] is.
The principal value of the amplitude of (1 + i) is
\[\text { If }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]
If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =
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
The value of \[(1 + i )^4 + (1 - i )^4\] is
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
If z is a complex number, then
If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on
Find a and b if a + 2b + 2ai = 4 + 6i
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 + sqrt(-3))/(4 + sqrt(-3))`
Evaluate the following : i35
Evaluate the following : i888
Evaluate the following : i116
Evaluate the following : i30 + i40 + i50 + i60
Show that 1 + i10 + i20 + i30 is a real number
