Advertisements
Advertisements
प्रश्न
Answer the following:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Advertisements
उत्तर
`3 + sqrt(-64) = 3 + sqrt(64)*sqrt(-1)`
= 3 + 8i
APPEARS IN
संबंधित प्रश्न
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
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
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Write the conjugates of the following complex number:
`-sqrt(-5)`
Find the value of i49 + i68 + i89 + i110
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Show that 1 + i10 + i100 − i1000 = 0
If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a2 = b and b2 = a
If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)
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+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = 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:
(2i3)2
Answer the following:
Simplify the following and express in the form a + ib:
(1 + 3i)2(3 + i)
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:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
Evaluate: i131 + i49
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
Multiplicative inverse of 1 + i is ______.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
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 ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
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`
i2 + i3 + ... + i4000 =
If z = 2 + i, then (z − 1) `(barz − 5) + (barz − 1)` (z − 5) is equal to ______.
