Advertisements
Advertisements
प्रश्न
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Advertisements
उत्तर
x = 1 – 4i
∴ x – 1 = – 4i
∴ (x – 1)2 = 16i2
∴ x2 – 2x + 1 = – 16 ...[∵ i2 = – 1]
∴ x2 – 2x + 17 = 0 ...(i)
x – 1
`x^2 – 2x + 17")"overline(x^3 - 3x^2 + 19x - 20)"`
x3 – 2x2 + 17x
– + –
– x2 + 2x – 20
– x2 + 2x – 17x
– + –
– 3
∴ x3 – 3x2 + 19x – 20
= (x2 – 2x + 17) (x – 1) – 3
= 0(x – 1) – 3 ...[From (i)]
= 0 – 3
∴ x3 – 3x2 + 19x – 20 = – 3
APPEARS IN
संबंधित प्रश्न
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
Write the conjugates of the following complex number:
`-sqrt(-5)`
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a2 = b and b2 = a
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Find the value of x and y which satisfy the following equation (x, y ∈ R).
`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
If z1, z2, z3 are complex numbers such that `|z_1| = |z_2| = |z_3| = |1/z_1 + 1/z_2 + 1/z_3|` = 1, then find the value of |z1 + z2 + z3|.
Locate the points for which 3 < |z| < 4.
State true or false for the following:
Multiplication of a non-zero complex number by i rotates it through a right angle in the anti-clockwise direction.
What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
State True or False for the following:
The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).
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)`
Show that `(-1 + sqrt3i)^3` is a real number.
