Advertisements
Advertisements
प्रश्न
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Advertisements
उत्तर
x = 1 – 4i
∴ x – 1 = – 4i
∴ (x – 1)2 = 16i2
∴ x2 – 2x + 1 = – 16 ...[∵ i2 = – 1]
∴ x2 – 2x + 17 = 0 ...(i)
x – 1
`x^2 – 2x + 17")"overline(x^3 - 3x^2 + 19x - 20)"`
x3 – 2x2 + 17x
– + –
– x2 + 2x – 20
– x2 + 2x – 17x
– + –
– 3
∴ x3 – 3x2 + 19x – 20
= (x2 – 2x + 17) (x – 1) – 3
= 0(x – 1) – 3 ...[From (i)]
= 0 – 3
∴ x3 – 3x2 + 19x – 20 = – 3
APPEARS IN
संबंधित प्रश्न
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 + 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")`
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Find the value of x and y which satisfy the following equation (x, y∈R).
`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
Select the correct answer from the given alternatives:
The value of is `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)` is equal to:
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"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
Evaluate: (1 + i)6 + (1 – i)3
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
If the real part of `(barz + 2)/(barz - 1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.
If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
If z is a complex number, then ______.
Show that `(-1 + sqrt3i)^3` is a real number.
