English

Find the multiplicative inverse of the complex number. –i

Advertisements
Advertisements

Question

Find the multiplicative inverse of the complex number.

–i 

Sum
Advertisements

Solution

multiplicative inverse of -i

= `1/i = 1/(-i) xx i/i = - i/i^2 = - i/(-1) = i`

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Complex Numbers and Quadratic Equations - EXERCISE 4.1 [Page 83]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 4 Complex Numbers and Quadratic Equations
EXERCISE 4.1 | Q 13. | Page 83

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`


Find the number of non-zero integral solutions of the equation `|1-i|^x  = 2^x`.


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


Find the value of i49 + i68 + i89 + i110 


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

`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`


Write the conjugates of the following complex number:

`-sqrt(-5)`


Write the conjugates of the following complex number:

`sqrt(5) - "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 = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)` 


If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1


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

`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i


Answer the following:

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

`(4 + 3"i")/(1 - "i")`


Answer the following:

Evaluate: (1 − i + i2)−15 


Answer the following:

Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real


Answer the following:

Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`


If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.


If `(x + iy)^(1/3)` = a + ib, where x, y, a, b ∈ R, show that `x/a - y/b` = –2(a2 + b2)


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|.


Locate the points for which 3 < |z| < 4.


If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.


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`.


What is the reciprocal of `3 + sqrt(7)i`.


If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.


Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.


The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.


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


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 ______.


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


If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` 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 ______.


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)`


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)`


i2 + i3 + ... + i4000 =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×