Advertisements
Advertisements
प्रश्न
Evaluate: `("i"^37 + 1/"i"^67)`
उत्तर
`"i"^37 + 1/"i"^67`
`= ("i"^104 + 1)/"i"^67`
= `(("i"^2)^52 + 1)/("i"^66 xx "i")`
= `((-1)^52 + 1)/(("i"^2)^33 "i")`
= `(1 + 1)/((-1)^33 "i")`
= `2/(-"i")`
= `(-2)/"i"`
= `(-2)/"i" xx "i"/"i"`
= `(-2"i")/"i"^2`
= 2i ...[∵ i2 = – 1]
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Simplify the following and express in the form a + ib:
(2i3)2
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
Write the conjugates of the following complex number:
`-sqrt(-5)`
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Simplify : `("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"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)
Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
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:
(2i3)2
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i
Answer the following:
Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real
The value of (2 + i)3 × (2 – i)3 is ______.
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
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 ______.
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
If the real part of `(barz + 2)/(barz - 1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
If a + ib = c + id, then ______.
If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) is equal to ______.
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 ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals 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)`
Simplify the following and express in the form a + ib.
`(3i^5+2i^7+i^9)/(i^6+2i^8+3i^18)`
