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
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Write the conjugates of the following complex number:
`-sqrt(-5)`
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")`
Answer the following:
Simplify the following and express in the form a + ib:
`5/2"i"(-4 - 3"i")`
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:
Simplify: `("i"^65 + 1/"i"^145)`
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)`
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
Evaluate the following:
i35
