Advertisements
Advertisements
प्रश्न
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)`
उत्तर
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
= `(3("i"^4*"i") + 2("i"^4*"i"^3) + ("i"^4)^2*"i")/("i"^4*"i"^2 + 2("i"^4)^2 + 3("i"^2)^9`
= `(3(1)* "i" + 2(1)(-"i") + (1)^2*"i")/((1)(-1) + 2(1)^2 + 3(-1)^9` ...[∵ i2 = – 1, i3 = – i, i4 = 1]
= `(3"i" - 2"i" + "i")/(-1 + 2 - 3)`
= `(2"i")/(-2)`
= – i
= 0 – i
APPEARS IN
संबंधित प्रश्न
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of i49 + i68 + i89 + i110
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
(2i3)2
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Write the conjugates of the following complex number:
cosθ + i sinθ
Evaluate: `("i"^37 + 1/"i"^67)`
If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1
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:
(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:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
The value of (2 + i)3 × (2 – i)3 is ______.
Evaluate: (1 + i)6 + (1 – i)3
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
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.
1 + i2 + i4 + i6 + ... + i2n is ______.
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"`
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
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.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
If z is a complex number, then ______.
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 ______.
A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.
Let z be a complex number such that `|(z - i)/(z + 2i)|` = 1 and |z| = `5/2`. Then the value of |z + 3i| is ______.
If α, β, γ and a, b, c are complex numbers such that `α/a + β/b + γ/c` = 1 + i and `a/α + b/β + c/γ` = 0, then the value of `α^2/a^2 + β^2/b^2 + γ^2/c^2` is equal to ______.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Find the value of `sqrt(-3) xx sqrt(-6)`
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
