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
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Answer the following:
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
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|.
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.
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
1 + i2 + i4 + i6 + ... + i2n is ______.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
The real value of α for which the expression `(1 - i sin alpha)/(1 + 2i sin alpha)` is purely real is ______.
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| 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)`
