हिंदी

State True or False for the following: Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.

Advertisements
Advertisements

प्रश्न

State True or False for the following:

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

Let z = x + yi

z.i = (x + yi)i = xi – y

Which rotates at angle of 180°.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Complex Numbers and Quadratic Equations - Exercise [पृष्ठ ९३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 5 Complex Numbers and Quadratic Equations
Exercise | Q 26.(ii) | पृष्ठ ९३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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

`3 + sqrt(-64)`


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

(1 + 3i)2 (3 + i)


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

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


Find the value of i49 + i68 + i89 + i110 


If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0


If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1


Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real


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:

`5/2"i"(-4 - 3"i")`


Answer the following:

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

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


Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0


Answer the following:

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


Answer the following:

Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`


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` = ______.


The value of (2 + i)3 × (2 – i)3 is ______.


Find the value of k if for the complex numbers z1 and z2, `|1 - barz_1z_2|^2 - |z_1 - z_2|^2 = k(1 - |z_1|^2)(1 - |"z"_2|^2)`


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.


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


If the real part of `(barz + 2)/(barz - 1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.


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


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


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


`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.


The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 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 ______.


Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.


Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`


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

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


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)`


Show that `(-1 + sqrt3i)^3` is a real number.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×