Advertisements
Advertisements
प्रश्न
Write the value of \[\sqrt{- 25} \times \sqrt{- 9}\].
उत्तर
\[\sqrt{- 25} \times \sqrt{- 9} = 5\sqrt{- 1} \times 3\sqrt{- 1}\]
\[ = 5i \times 3i\]
\[ = 15 i^2 \]
\[ = - 15\]
Hence,
\[\sqrt{- 25} \times \sqrt{- 9} = - 15\]
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
Evaluate the following:
\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]
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:
i30 + i80 + i120
Express the following complex number in the standard form a + i b:
\[(1 + i)(1 + 2i)\]
Express the following complex number in the standard form a + i b:
\[\left( \frac{1}{1 - 4i} - \frac{2}{1 + i} \right)\left( \frac{3 - 4i}{5 + i} \right)\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Re \[\left( \frac{z_1 z_2}{z_1} \right)\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Im `(1/(z_1overlinez_1))`
If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.
Find the real values of θ for which the complex number \[\frac{1 + i cos\theta}{1 - 2i cos\theta}\] is purely real.
If \[\frac{z - 1}{z + 1}\] is purely imaginary number (\[z \neq - 1\]), find the value of \[\left| z \right|\].
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 1 − i in polar form.
Write the least positive integral value of n for which \[\left( \frac{1 + i}{1 - i} \right)^n\] is real.
The polar form of (i25)3 is
If a = cos θ + i sin θ, then \[\frac{1 + a}{1 - a} =\]
If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals
If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =
If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =
The argument of \[\frac{1 - i}{1 + i}\] is
\[\frac{1 + 2i + 3 i^2}{1 - 2i + 3 i^2}\] equals
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
The complex number z which satisfies the condition \[\left| \frac{i + z}{i - z} \right| = 1\] lies on
If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on
Simplify : `4sqrt(-4) + 5sqrt(-9) - 3sqrt(-16)`
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:
`(2 + sqrt(-3))/(4 + sqrt(-3))`
Show that 1 + i10 + i20 + i30 is a real number
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)`.
Match the statements of column A and B.
Column A | Column B |
(a) The value of 1 + i2 + i4 + i6 + ... i20 is | (i) purely imaginary complex number |
(b) The value of `i^(-1097)` is | (ii) purely real complex number |
(c) Conjugate of 1 + i lies in | (iii) second quadrant |
(d) `(1 + 2i)/(1 - i)` lies in | (iv) Fourth quadrant |
(e) If a, b, c ∈ R and b2 – 4ac < 0, then the roots of the equation ax2 + bx + c = 0 are non real (complex) and |
(v) may not occur in conjugate pairs |
(f) If a, b, c ∈ R and b2 – 4ac > 0, and b2 – 4ac is a perfect square, then the roots of the equation ax2 + bx + c = 0 |
(vi) may occur in conjugate pairs |
Show that `(-1+sqrt3i)^3` is a real number.