मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • Positive

  • Negative

  • 0

  • Can not be evaluated

MCQ
रिकाम्या जागा भरा

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Complex Numbers and Quadratic Equations - Solved Examples [पृष्ठ ८९]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 28 | पृष्ठ ८९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the multiplicative inverse of the complex number.

`sqrt5 + 3i`


Show that 1 + i10 + i20 + i30 is a real number.


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:

cosθ + i sinθ


Find the value of i + i2 + i3 + i4 


Show that 1 + i10 + i100 − i1000 = 0 


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 + 2i + 15i6y = 7x + i3 (y + 4), find x + y


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:

Evaluate: (1 − i + i2)−15 


Answer the following:

If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1


Answer the following:

Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`


If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.


If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.


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`.


If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.


If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.


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


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).


Find `|(1 + i) ((2 + i))/((3 + i))|`.


A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.


Let x, y ∈ R, then x + iy is a non-real complex number if ______.


If z is a complex number, then ______.


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


The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.


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×