English

Write the conjugates of the following complex numbers: 3 + i

Advertisements
Advertisements

Question

Write the conjugates of the following complex number:

3 + i

One Line Answer
Advertisements

Solution

Conjugate of (3 + i) is (3 – i)

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

RELATED QUESTIONS

Find the multiplicative inverse of the complex number:

4 – 3i


Find the multiplicative inverse of the complex number.

`sqrt5 + 3i`


Find the multiplicative inverse of the complex number.

–i 


Find the value of i49 + i68 + i89 + i110 


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

(2 + 3i)(1 – 4i)


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:

`(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"`


Find the value of i49 + i68 + i89 + i110 


Simplify:

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


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


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:

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:

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


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:

Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i


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 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 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 the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.


The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.


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


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


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


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


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 ______.


Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.


The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.


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)`


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×