Advertisements
Advertisements
प्रश्न
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Advertisements
उत्तर
x = 2 + 3i
∴ x – 2 = 3i
∴ `(x - 2)^2 = (3i)^2`
∴ (x – 2)2 = 9i2
∴ x2 – 4x + 4 = 9(– 1) ...[∵ i2 = – 1]
∴ x2 – 4x + 13 = 0 ...(i)
x + 3
`x^2 – 4x + 13")"overline(x^3 - x^2 + x + 46)"`
x3 – 4x2 + 13x
– + –
3x2 – 12x + 46
3x2 – 12x + 39
– + –
7
∴x3 – x2 + x + 46
= (x2 – 4x + 13)(x + 3) + 7
= 0(x + 3) + 7 ...[From (i)]
= 7.
APPEARS IN
संबंधित प्रश्न
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
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.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
State True or False for the following:
Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.
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 ______.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal 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)`
i2 + i3 + ... + i4000 =
