Advertisements
Advertisements
प्रश्न
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:
पर्याय
−2
1
0
−1
Advertisements
उत्तर
−1
Explanation:
`= ("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)`
`= (i^4 + i^2 + i^4 + i^2 + i^4)/(i^2 + i^4 + i^2 + i^4 + i^2) `
`= (3 - 2)/ (- 3 + 2)`
`= 1/-1`
= -1
APPEARS IN
संबंधित प्रश्न
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Write the conjugates of the following complex number:
5i
If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Select the correct answer from the given alternatives:
If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :
Answer the following:
Simplify the following and express in the form a + ib:
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
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:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Answer the following:
Evaluate: i131 + i49
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
Locate the points for which 3 < |z| < 4.
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.
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
What is the principal value of amplitude of 1 – i?
If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
If `((1 + i)/(1 - i))^x` = 1, then ______.
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
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 ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
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)`
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)`
Find the value of `sqrt(-3) xx sqrt(-6)`
Show that `(-1 + sqrt3i)^3` is a real number.
