Advertisements
Advertisements
प्रश्न
State True or False for the following:
The order relation is defined on the set of complex numbers.
पर्याय
True
False
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: i–39
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Evaluate the following:
\[i^{30} + i^{40} + i^{60}\]
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of the following expression:
1+ i2 + i4 + i6 + i8 + ... + i20
Find the value of the following expression:
(1 + i)6 + (1 − i)3
Find the real value of x and y, if
\[(3x - 2iy)(2 + i )^2 = 10(1 + i)\]
Find the multiplicative inverse of the following complex number:
\[(1 + i\sqrt{3} )^2\]
If \[a = \cos\theta + i\sin\theta\], find the value of \[\frac{1 + a}{1 - a}\].
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 \[\left| z_1 + z_2 + z_3 \right|\] .
Write (i25)3 in polar form.
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 \[\frac{\left( a^2 + 1 \right)^2}{2a - i} = x + iy\] find the value of \[x^2 + y^2\].
Write the sum of the series \[i + i^2 + i^3 + . . . .\] upto 1000 terms.
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 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
The value of \[(1 + i )^4 + (1 - i )^4\] is
Find a and b if (a – b) + (a + b)i = a + 5i
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:
`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"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
Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:
`(4"i"^8 - 3"i"^9 + 3)/(3"i"^11 - 4"i"^10 - 2)`
Evaluate the following : i35
Evaluate the following : `1/"i"^58`
Evaluate the following : i30 + i40 + i50 + i60