Advertisements
Advertisements
प्रश्न
Write the conjugates of the following complex number:
5i
Advertisements
उत्तर
Conjugate of 5i is – 5i
APPEARS IN
संबंधित प्रश्न
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Simplify the following and express in the form a + ib:
(2i3)2
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Show that 1 + i10 + i100 − i1000 = 0
If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
Find the value of x and y which satisfy the following equation (x, y∈R).
`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
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
Answer the following:
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"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 z = `((-1 + sqrt(-3))/2)^3` is a rational number
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
Locate the points for which 3 < |z| < 4.
What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
1 + i2 + i4 + i6 + ... + i2n is ______.
The equation |z + 1 – i| = |z – 1 + i| represents a ______.
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.
Solve the equation |z| = z + 1 + 2i.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
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 ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
If α, β, γ and a, b, c are complex numbers such that `α/a + β/b + γ/c` = 1 + i and `a/α + b/β + c/γ` = 0, then the value of `α^2/a^2 + β^2/b^2 + γ^2/c^2` is equal to ______.
If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.
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)`
Find the value of `sqrt(-3) xx sqrt(-6)`
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)`
