Advertisements
Advertisements
Question
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Advertisements
Solution
Multiplicative inverse of `sqrt5 + 3i`
= `1/(sqrt5 + 3i) = 1/(sqrt5 + 3i) xx (sqrt5 - 3i)/ (sqrt5 - 3i)`
= `(sqrt5 - 3i)/(5 - 9i^2)`
= `(sqrt5 - 3i)/(5 +9)`
= `(sqrt(5) - 3i)/14`
= `sqrt5/14 - 3/14 i`
RELATED QUESTIONS
Find the multiplicative inverse of the complex number.
–i
If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.
Find the value of i + i2 + i3 + i4
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Find the value of i + i2 + i3 + i4
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0
Find the value of x and y which satisfy the following equation (x, y ∈ R).
`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
Select the correct answer from the given alternatives:
If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :
Answer the following:
Simplify the following and express in the form a + ib:
`5/2"i"(-4 - 3"i")`
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:
Evaluate: i131 + i49
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
Find the value of k if for the complex numbers z1 and z2, `|1 - barz_1z_2|^2 - |z_1 - z_2|^2 = k(1 - |z_1|^2)(1 - |"z"_2|^2)`
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 value of `(i^(4n + 1) -i^(4n - 1))/2`?
What is the reciprocal of `3 + sqrt(7)i`.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
1 + i2 + i4 + i6 + ... + i2n is ______.
If the real part of `(barz + 2)/(barz - 1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
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.
If a + ib = c + id, then ______.
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 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 ______.
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.
