Advertisements
Advertisements
प्रश्न
Write the conjugates of the following complex number:
5i
Advertisements
उत्तर
Conjugate of 5i is – 5i
APPEARS IN
संबंधित प्रश्न
Find the value of i49 + i68 + i89 + i110
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Write the conjugates of the following complex number:
cosθ + i sinθ
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
Prove that `(1 + "i")^4 xx (1 + 1/"i")^4` = 16
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
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
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:
`3 + sqrt(-64)`
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Answer the following:
Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i
Answer the following:
Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
Locate the points for which 3 < |z| < 4.
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Show that `(-1 + sqrt3i)^3` is a real number.
i2 + i3 + ... + i4000 =
