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
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:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Write the conjugates of the following complex number:
5i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1
Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real
Find the value of x and y which satisfy the following equation (x, y∈R).
If x + 2i + 15i6y = 7x + i3 (y + 4), find x + y
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
Answer the following:
Simplify: `("i"^65 + 1/"i"^145)`
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
State true or false for the following:
The argument of the complex number z = `(1 + i sqrt(3))(1 + i)(cos theta + i sin theta)` is `(7pi)/12 + theta`.
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
Solve the equation |z| = z + 1 + 2i.
Let z be a complex number such that `|(z - i)/(z + 2i)|` = 1 and |z| = `5/2`. Then the value of |z + 3i| 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)`
Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`
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)`
