Advertisements
Advertisements
Question
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
Solution
x + 2 = `- sqrt(3)"i"` ⇒ x2 + 4x + 7 = 0
Therefore, 2x4 + 5x3 + 7x2 – x + 41
= (x2 + 4x + 7)(2x2 – 3x + 5) + 6
= 0 × (2x2 – 3x + 5) + 6
= 6
APPEARS IN
RELATED QUESTIONS
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
Write the conjugates of the following complex number:
cosθ + i sinθ
Find the value of i49 + i68 + i89 + i110
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Show that 1 + i10 + i100 − i1000 = 0
Answer the following:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
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:
(1 + 3i)2(3 + i)
Answer the following:
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Answer the following:
Simplify the following and express in the form a + ib:
`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`
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:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Locate the points for which 3 < |z| < 4.
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
State true or false for the following:
If n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
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 α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
If α, β, γ and a, b, c are complex numbers such that `α/a + β/b + γ/c` = 1 + i and `a/α + b/β + c/γ` = 0, then the value of `α^2/a^2 + β^2/b^2 + γ^2/c^2` 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)`
