Advertisements
Advertisements
प्रश्न
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
पर्याय
`-3sqrt(2)`
`3sqrt(2)`
`3sqrt(2)"i"`
`-3sqrt(2)"i"`
उत्तर
`-3sqrt(2)`
Explanation;
`sqrt(-3) sqrt(-6) = (sqrt(3)"i") (sqrt(6)"i")`
= `3sqrt(2) (-1)`
`-3sqrt(2)`.
APPEARS IN
संबंधित प्रश्न
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the value of i49 + i68 + i89 + i110
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Evaluate: `("i"^37 + 1/"i"^67)`
Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
Answer the following:
Simplify the following and express in the form a + ib:
(2i3)2
Answer the following:
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i
Answer the following:
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
Evaluate: (1 + i)6 + (1 – i)3
Locate the points for which 3 < |z| < 4.
Find the value of k if for the complex numbers z1 and z2, `|1 - barz_1z_2|^2 - |z_1 - z_2|^2 = k(1 - |z_1|^2)(1 - |"z"_2|^2)`
State true or false for the following:
The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.
Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.
Solve the equation |z| = z + 1 + 2i.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
Which of the following is correct for any two complex numbers z1 and z2?
If a + ib = c + id, then ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.
Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`