मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Write the conjugates of the following complex number: 5i - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the conjugates of the following complex number:

5i

एका वाक्यात उत्तर

उत्तर

Conjugate of 5i is – 5i

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Complex Numbers - Exercise 1.1 [पृष्ठ ६]

APPEARS IN

संबंधित प्रश्‍न

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`


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

`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`


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

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


Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.


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:

`-sqrt(-5)`


Write the conjugates of the following complex number:

cosθ + i sinθ


Find the value of i + i2 + i3 + i4 


Simplify : `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)`


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 + 2y) + (2x − 3y)i + 4i = 5


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:

If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :


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:

(2 + 3i)(1 − 4i)


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")`


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


The value of (2 + i)3 × (2 – i)3 is ______.


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


State true or false for the following:

Multiplication of a non-zero complex number by i rotates it through a right angle in the anti-clockwise direction.


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 n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.


What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?


Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.


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


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


If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.


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


Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.


If `((1 + i)/(1 - i))^x` = 1, then ______.


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


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 ______.


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

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


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.

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

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


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×