English

1 + i2 + i4 + i6 + ... + i2n is ______. - Mathematics

Advertisements
Advertisements

Question

1 + i2 + i4 + i6 + ... + i2n is ______.

Options

  • Positive

  • Negative

  • 0

  • Can not be evaluated

MCQ
Fill in the Blanks
Advertisements

Solution

1 + i2 + i4 + i6 + ... + i2n is can not be evaluated.

Explanation:

1 + i2 + i4 + i6 + ... + i2n = 1 – 1 + 1 – 1 + ... (–1)n

Which can not be evaluated unless n is known.

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Complex Numbers and Quadratic Equations - Solved Examples [Page 89]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 28 | Page 89

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.


Simplify the following and express in the form a + ib:

`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`


Write the conjugates of the following complex number:

3 – i


Write the conjugates of the following complex number:

`sqrt(2) + sqrt(3)"i"`


Write the conjugates of the following complex number:

cosθ + i sinθ


Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20


Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`


If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)


Find the value of x and y which satisfy the following equation (x, y∈R).

If x(1 + 3i) + y(2 − i) − 5 + i3 = 0, find x + y


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:

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 equation for x, y ∈ R:

(4 − 5i)x + (2 + 3i)y = 10 − 7i


Answer the following:

Solve the following equation for x, y ∈ R:

`(x + "i"y)/(2 + 3"i")` = 7 – i


Answer the following:

Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i


Answer the following:

Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i


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:

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:

If three complex numbers z1, z2 and z3 are in A.P., then they lie on a circle in the complex plane.


What is the principal value of amplitude of 1 – i?


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.


Solve the equation |z| = z + 1 + 2i.


The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.


If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.


State True or False for the following:

For any complex number z the minimum value of |z| + |z – 1| is 1.


If z is a complex number, then ______.


Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.


If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = `|1/z_1 + 1/z_2 + 1/z_3|` = 1, then |z1 + z2 + z3| is ______.


If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.


A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.


`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.


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)`


Show that `(-1 + sqrt3 i)^3` is a real number.


Simplify the following and express in the form a + ib.

`(3i^5 + 2i^7 + i^9) / (i^6 + 2i^8 + 3i^18)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×