Advertisements
Advertisements
प्रश्न
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Advertisements
उत्तर
x = `25/(3 - 4"i")`
∴ x = `(25(3 + 4"i"))/((3 - 4"i")(3 + 4"i")`
= `(25(3 + 4"i"))/(9 - 16"i"^2)`
= `(25(3 + 4"i"))/(9 - 16(-1))` ...[∵ i2 = – 1]
= `(25(3 + 4"i"))/25`
∴ x = 3 + 4
∴ x – 3 = 4i
∴ (x – 3)2 = 16i2
∴ x2 – 6x + 9 = 16(– 1) ...[∵ i2 = – 1]
∴ x2 – 6x + 25 = 0
2x + 1
`x^2 – 6x + 25")"overline(2x^3 - 11x^2 + 44x + 27)"`
2x3 – 12x2 + 50x
– + –
x2 – 6x + 27
x2 – 6x + 25
– + –
2
∴ 2x3 – 11x2 + 44x + 27
= (x2 – 6x + 25) (2x + 1) + 2
= 0.(2x + 1) + 2 ...[From (i)]
= 0 + 2
= 2
APPEARS IN
संबंधित प्रश्न
Simplify the following and express in the form a + ib:
(2i3)2
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
Simplify the following and express in the form a + ib:
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Evaluate: `("i"^37 + 1/"i"^67)`
Answer the following:
Simplify the following and express in the form a + ib:
(2 + 3i)(1 − 4i)
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
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.
For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
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.
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).
If a + ib = c + id, then ______.
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 ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| 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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^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.
`(3i^5+2i^7+i^9)/(i^6+2i^8+3i^18)`
