Advertisements
Advertisements
Question
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
Advertisements
Solution
The sum of the series i + i2 + i3 + ... upto 1000 terms is 0.
Explanation:
i + i2 + i3 + ... upto 1000 terms
= i + i2 + i3 + ... + i1000
= 0
`[sum_(n = 1)^1000 i^n = 0]`
APPEARS IN
RELATED QUESTIONS
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Find the value of i49 + i68 + i89 + i110
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Prove that `(1 + "i")^4 xx (1 + 1/"i")^4` = 16
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 + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "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
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:
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
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
If z1, z2, z3 are complex numbers such that `|z_1| = |z_2| = |z_3| = |1/z_1 + 1/z_2 + 1/z_3|` = 1, then find the value of |z1 + z2 + z3|.
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
The equation |z + 1 – i| = |z – 1 + i| represents a ______.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
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.
Solve the equation |z| = z + 1 + 2i.
If |z + 1| = z + 2(1 + i), then find z.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
Multiplicative inverse of 1 + i is ______.
State True or False for the following:
The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).
The real value of α for which the expression `(1 - i sin alpha)/(1 + 2i sin alpha)` is purely real is ______.
If z is a complex number, then ______.
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)`
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)`
