Advertisements
Advertisements
प्रश्न
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Advertisements
उत्तर
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
= `(i^584 (i^8 + i^6 + i^4 + i^2 + 1))/(i^574 (i^8 + i^6 + i^4 + i^2 + 1))`
= `(i^584)/(i^574)`
= i10
= (i2)5
= (–1)5
= – 1
APPEARS IN
संबंधित प्रश्न
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Find the value of i49 + i68 + i89 + i110
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Find the value of x and y which satisfy the following equation (x, y∈R).
`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
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:
Simplify the following and express in the form a + ib:
(2 + 3i)(1 − 4i)
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:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Answer the following:
Find the real numbers x and y such that `x/(1 + 2"i") + y/(3 + 2"i") = (5 + 6"i")/(-1 + 8"i")`
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
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.
What is the reciprocal of `3 + sqrt(7)i`.
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
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 ______.
If a + ib = c + id, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
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 α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
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)`
Show that `(-1 + sqrt3 i)^3` is a real number.
i2 + i3 + ... + i4000 =
