Advertisements
Advertisements
प्रश्न
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
Advertisements
उत्तर
`(1/(1-4i) - 2/(1+i))((3-4i)/(5+i)) = [((1 + i) - 2(1 + 4i))/((1 - 4i)(1 + i)]] [ (3 - 4i)/(5 +i)]`
= `[(1 + i - 2 + 8i)/(1 + i - 4i - 4i^2)][(3 - 4i)/(5 +i)] = [(- 1 + 9i)/(5 - 3i)] [(3 - 4i)/(5 + i)]`
= `[( - 3 + 4i + 27i - 36i^2)/(25 + 5i - 15i - 3i^2)] = (33 + 31i)/(28 - 10i) =(33 + 31i)/(2(14 - 5i)`
= `(33 + 31i )/(2(14 - 5i)) xx (14 + 5i)/(14 + 5i)`
= `(462 + 165i + 434i + 155i^2)/(2[(14)^2 - (5i)^2]] xx (307 + 599i)/(2(196 - 25i^2)`
= `(307 + 599i)/(2(221)) = (307 + 599i)/442 = 307/442 + (599i)/442`
APPEARS IN
संबंधित प्रश्न
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.
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Simplify the following and express in the form a + ib:
(2i3)2
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Write the conjugates of the following complex number:
3 – i
Write the conjugates of the following complex number:
5i
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Prove that `(1 + "i")^4 xx (1 + 1/"i")^4` = 16
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).
`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
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:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Answer the following:
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)`
Answer the following:
Evaluate: (1 − i + i2)−15
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 z1, z2, z3 are complex numbers such that `|z_1| = |z_2| = |z_3| = |1/z_1 + 1/z_2 + 1/z_3|` = 1, then find the value of |z1 + z2 + z3|.
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.
State true or false for the following:
If n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
1 + i2 + i4 + i6 + ... + i2n is ______.
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
State True or False for the following:
The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).
The value of `(z + 3)(barz + 3)` is equivalent to ______.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
Which of the following is correct for any two complex numbers z1 and z2?
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
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)`
