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
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Find the value of i + i2 + i3 + i4
Write the conjugates of the following complex number:
5i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Evaluate: `("i"^37 + 1/"i"^67)`
If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)
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: `("i"^65 + 1/"i"^145)`
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`.
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.
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.
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`
Find the value of `sqrt(-3) xx sqrt(-6)`
