Advertisements
Advertisements
प्रश्न
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
उत्तर
(x + iy) (5 + 6i) = 2 + 3i
∴ x + iy = `(2 + 3"i")/(5 + 6"i")`
∴ x + iy = `((2 + 3"i")(5 - 6"i"))/((5 + 6"i")(5 - 6"i"))`
= `(10 - 12"i" + 15"i" - 18"i"^2)/(25 - 36"i"^2)`
= `(10 + 3"i" - 18(-1))/(25 - 36(-1))`
∴ x + iy = `(28 + 3"i")/61`
= `28/61 + 3/61"i"`
Equating real and imaginary parts, we get
x = `28/61` and y = `3/61`
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number:
4 – 3i
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a2 = b and b2 = a
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
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
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`.
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
What is the principal value of amplitude of 1 – i?
1 + i2 + i4 + i6 + ... + i2n is ______.
The equation |z + 1 – i| = |z – 1 + i| represents a ______.
Solve the equation |z| = z + 1 + 2i.
If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.
Multiplicative inverse of 1 + i is ______.
If `((1 + i)/(1 - i))^x` = 1, then ______.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.
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 ______.
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.
`(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)`
Find the value of `sqrt(-3) xx sqrt(-6)`
