Advertisements
Advertisements
प्रश्न
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Advertisements
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.
`sqrt5 + 3i`
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Simplify the following and express in the form a + ib:
(2i3)2
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Find the value of i + i2 + i3 + i4
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Show that 1 + i10 + i100 − i1000 = 0
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).
(x + 2y) + (2x − 3y)i + 4i = 5
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
Answer the following:
Simplify the following and express in the form a + ib:
`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`
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")`
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
State true or false for the following:
The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.
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.
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
What is the reciprocal of `3 + sqrt(7)i`.
What is the principal value of amplitude of 1 – i?
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = `|1/z_1 + 1/z_2 + 1/z_3|` = 1, then |z1 + z2 + z3| 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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Show that `(-1 + sqrt3 i)^3` is a real number.
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)`
