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
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the value of i49 + i68 + i89 + i110
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
`-sqrt(-5)`
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Find the value of i + i2 + i3 + i4
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Evaluate: `("i"^37 + 1/"i"^67)`
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).
`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
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:
(1 + 3i)2(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")`
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
Locate the points for which 3 < |z| < 4.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
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:
The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
If |z + 1| = z + 2(1 + i), then find z.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
Which of the following is correct for any two complex numbers z1 and z2?
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
If α, β, γ and a, b, c are complex numbers such that `α/a + β/b + γ/c` = 1 + i and `a/α + b/β + c/γ` = 0, then the value of `α^2/a^2 + β^2/b^2 + γ^2/c^2` is equal to ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.
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)`
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)`
