Advertisements
Advertisements
Question
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
Options
`-3sqrt(2)`
`3sqrt(2)`
`3sqrt(2)"i"`
`-3sqrt(2)"i"`
Advertisements
Solution
`-3sqrt(2)`
Explanation;
`sqrt(-3) sqrt(-6) = (sqrt(3)"i") (sqrt(6)"i")`
= `3sqrt(2) (-1)`
`-3sqrt(2)`.
APPEARS IN
RELATED QUESTIONS
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
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:
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
cosθ + i sinθ
Show that 1 + i10 + i100 − i1000 = 0
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
Answer the following:
Simplify the following and express in the form a + ib:
(2i3)2
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.
What is the reciprocal of `3 + sqrt(7)i`.
What is the principal value of amplitude of 1 – i?
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
If |z + 1| = z + 2(1 + i), then find z.
Multiplicative inverse of 1 + i is ______.
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) is equal to ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9) / (i^6 + 2i^8 + 3i^18)`
Simplify the following and express in the form a + ib.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Show that `(-1 + sqrt3i)^3` is a real number.
