Advertisements
Advertisements
प्रश्न
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
उत्तर
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
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
–i
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
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:
`(4 + 3"i")/(1 - "i")`
Answer the following:
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
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/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
The value of (2 + i)3 × (2 – i)3 is ______.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
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.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 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 ______.
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.
`(3i^5+2i^7+i^9)/(i^6+2i^8+3i^18)`