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
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
(2i3)2
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real
Answer the following:
Simplify the following and express in the form a + ib:
(2 + 3i)(1 − 4i)
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:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
If `(x + iy)^(1/3)` = a + ib, where x, y, a, b ∈ R, show that `x/a - y/b` = –2(a2 + b2)
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.
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?
Number of solutions of the equation z2 + |z|2 = 0 is ______.
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.
For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
Which of the following is correct for any two complex numbers z1 and z2?
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| is equal to ______.
Show that `(-1 + sqrt3 i)^3` is a real number.
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)`
Evaluate the following:
i35
If z = 2 + i, then (z − 1) `(barz − 5) + (barz − 1)` (z − 5) is equal to ______.
