Advertisements
Advertisements
प्रश्न
What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?
उत्तर
i, because `(i^(4n + 1) -i^(4n - 1))/2 = (i^(4n)i - i^(4n)i^-i)/2`
= `(i - 1/i)/2`
= `(i^2 - 1)/(2i)`
= `(-2)/(2i)`
= i
APPEARS IN
संबंधित प्रश्न
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "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")`
Write the conjugates of the following complex number:
3 + i
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Evaluate: `("i"^37 + 1/"i"^67)`
Answer the following:
Simplify the following and express in the form a + ib:
(2i3)2
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:
`(4 + 3"i")/(1 - "i")`
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:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
Evaluate: (1 + i)6 + (1 – i)3
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of 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 value of `sqrt(-25) xx sqrt(-9)` is ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
If `((1 + i)/(1 - i))^x` = 1, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
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, 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 ______.
Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`
Show that `(-1 + sqrt3 i)^3` is a real number.
Show that `(-1 + sqrt3i)^3` is a real number.
