Advertisements
Advertisements
प्रश्न
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Advertisements
उत्तर
z1 = 2 – i, z2 = –2 + i
`((z_1z_2)/barz_1) = ((2 - i)(-2 +i))/(2 -i) = (-(2 - i)(2 -i))/(2 + i)`
= `- (2-i)^2/(2 + i) = (- (4 + i^2 - 4i))/(2 + i)`
= `(-(4 - 1 - 4i))/((2 + i)) = -(3 - 4i)/(2 + i)`
= `-(3 - 4i)/(2 + i) xx (2 - i)/(2 - i)`
= `(- 6 - 4i^2 + 3i + 8i)/(4 - i^2) = (- 6 + 4 + 11i)/(4 + 1)`
= `(- 2 + 11i)/5 = - 2/5 + 11/5 i`
Re`((z_1z_2)/barz_1) = - 2/5`
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: 3(7 + i7) + i(7 + i7)
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:
(ii) i528
Evaluate the following:
\[\frac{1}{i^{58}}\]
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:
\[(1 + 2i )^{- 3}\]
If \[\left( 1 + i \right)z = \left( 1 - i \right) \bar{z}\],then show that \[z = - i \bar{z}\].
Solve the system of equations \[\text { Re }\left( z^2 \right) = 0, \left| z \right| = 2\].
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 \[\left| z_1 + z_2 + z_3 \right|\] .
Express the following complex in the form r(cos θ + i sin θ):
1 + i tan α
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 \[z_1 = - \bar{{z_2}}\].
Find the principal argument of \[\left( 1 + i\sqrt{3} \right)^2\] .
Find z, if \[\left| z \right| = 4 \text { and }\arg(z) = \frac{5\pi}{6} .\]
If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.
Write the value of \[\sqrt{- 25} \times \sqrt{- 9}\].
Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].
If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to
The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is
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
If \[x + iy = \frac{3 + 5i}{7 - 6i},\] then y =
If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =
The amplitude of \[\frac{1}{i}\] is equal to
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`
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"))`
Evaluate the following : i–888
Show that 1 + i10 + i20 + i30 is a real number
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
State True or False for the following:
The order relation is defined on the set of complex numbers.
The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.
