मराठी

Locate the points for which 3 < |z| < 4.

Advertisements
Advertisements

प्रश्न

Locate the points for which 3 < |z| < 4.

बेरीज
Advertisements

उत्तर

|z| < 4 ⇒ x2 + y2 < 16 which is the interior of circle with centre at origin and radius 4 units And |z| > 3 ⇒ x2 + y2 > 9 which is exterior of circle with centre at origin and radius 3 units.

Hence 3 < |z| < 4 is the portion between two circles x2 + y2 = 9 and x2 + y2 = 16.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Complex Numbers and Quadratic Equations - Solved Examples [पृष्ठ ८१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 10 | पृष्ठ ८१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the multiplicative inverse of the complex number:

4 – 3i


Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`


Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.


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:

`(4 + 3"i")/(1 - "i")`


Write the conjugates of the following complex number:

`sqrt(5) - "i"`


Evaluate: `("i"^37 + 1/"i"^67)`


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 + 2y) + (2x − 3y)i + 4i = 5


Find the value of x and y which satisfy the following equation (x, y∈R).

If x + 2i + 15i6y = 7x + i3 (y + 4), find x + y


Answer the following:

Simplify the following and express in the form a + ib:

`3 + sqrt(-64)`


Answer the following:

If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1


Answer the following:

Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real


If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.


If `(x + iy)^(1/3)` = a + ib, where x, y, a, b ∈ R, show that `x/a - y/b` = –2(a2 + b2)


If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.


State true or false for the following:

Multiplication of a non-zero complex number by i rotates it through a right angle in the anti-clockwise direction.


1 + i2 + i4 + i6 + ... + i2n is ______.


Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.


If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).


If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.


If |z + 1| = z + 2(1 + i), then find z.


Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.


The number `(1 - i)^3/(1 - i^2)` is equal to ______.


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.


State True or False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.


Find `|(1 + i) ((2 + i))/((3 + i))|`.


A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.


Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.


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 ______.


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 ______.


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.

`(3i^5+2i^7+i^9)/(i^6+2i^8+3i^18)`


Simplify the following and express in the form a+ib.

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×