English

Write the conjugates of the following complex number: -5-7i

Advertisements
Advertisements

Question

Write the conjugates of the following complex number:

`-sqrt(5) - sqrt(7)"i"`

One Line Answer
Advertisements

Solution

Conjugate of `(-sqrt(5) - sqrt(7)"i")` is `(-sqrt(5) + sqrt(7)"i")`

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

RELATED QUESTIONS

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:

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


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:

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


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


If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)


If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0


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


Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real


Answer the following:

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

`3 + sqrt(-64)`


Answer the following:

Solve the following equation for x, y ∈ R:

`(x + "i"y)/(2 + 3"i")` = 7 – i


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")`


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 |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is


The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______


The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real 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:

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


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?


If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.


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


If z = x + iy, then show that `z  barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.


If |z + 1| = z + 2(1 + i), then find z.


If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.


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


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.


The value of `(z + 3)(barz + 3)` is equivalent to ______.


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


If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.


If z = 2 + i, then (z − 1) `(barz − 5) + (barz − 1)` (z − 5) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×