Advertisements
Advertisements
प्रश्न
State True or False for the following:
The order relation is defined on the set of complex numbers.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Comparison of two purely imaginary complex numbers is not possible. However, the two purely real complex numbers can be compared.
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)
Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`
Evaluate the following:
i457
Evaluate the following:
\[i^{30} + i^{40} + i^{60}\]
Express the following complex number in the standard form a + i b:
\[\frac{(1 + i)(1 + \sqrt{3}i)}{1 - i}\] .
Find the real value of x and y, if
\[(3x - 2iy)(2 + i )^2 = 10(1 + i)\]
Find the real value of x and y, if `((1+i)x-2i)/(3+i) + ((2-3i)y+i)/(3-i) = i, xy ∈ R, i = sqrt-1`
If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.
If \[\left( 1 + i \right)z = \left( 1 - i \right) \bar{z}\],then show that \[z = - i \bar{z}\].
Write (i25)3 in polar form.
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 \[z_1 = - \bar{{z_2}}\].
Write the least positive integral value of n for which \[\left( \frac{1 + i}{1 - i} \right)^n\] is real.
If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.
If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].
If n ∈ \[\mathbb{N}\] then find the value of \[i^n + i^{n + 1} + i^{n + 2} + i^{n + 3}\] .
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
The argument of \[\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\] is
If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =
The argument of \[\frac{1 - i}{1 + i}\] is
The amplitude of \[\frac{1 + i\sqrt{3}}{\sqrt{3} + i}\] is
A real value of x satisfies the equation \[\frac{3 - 4ix}{3 + 4ix} = a - ib (a, b \in \mathbb{R}), if a^2 + b^2 =\]
Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`
Find a and b if (a – b) + (a + b)i = a + 5i
Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i
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:
`("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:
(1 + i)−3
Evaluate the following : i35
Evaluate the following : i93
Evaluate the following : i116
Evaluate the following : `1/"i"^58`
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
If z1 and z2 both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.
If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).
