English

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

Advertisements
Advertisements

Question

Write the conjugates of the following complex number:

`sqrt(5) - "i"`

One Line Answer

Solution

The conjugates of `sqrt(5) - "i"` is `sqrt(5) + "i"`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Complex Numbers - Exercise 1.1 [Page 6]

RELATED QUESTIONS

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.


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


Find the value of i49 + i68 + i89 + i110 


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

`5/2"i"(- 4 - 3 "i")`


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

(1 + 3i)2 (3 + i)


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

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


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)`


Is (1 + i14 + i18 + i22) a real number? Justify your answer


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

`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`


Answer the following:

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

(1 + 3i)2(3 + i)


Answer the following:

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

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


Solve the following equation for x, y ∈ R:

2x + i9y (2 + i) = xi7 + 10i16


Answer the following:

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


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


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|.


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


Number of solutions of the equation z2 + |z|2 = 0 is ______.


For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`


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


If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.


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 + 2(1 + i), then find 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|`.


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


State True or False for the following:

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


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


Which of the following is correct for any two complex numbers z1 and z2?


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


If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) is equal to ______.


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


Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals 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`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×