हिंदी

Let x, y ∈ R, then x + iy is a non-real complex number if ______.

Advertisements
Advertisements

प्रश्न

Let x, y ∈ R, then x + iy is a non-real complex number if ______.

विकल्प

  • x = 0

  • y = 0

  • x ≠ 0

  • y ≠ 0

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

Let x, y ∈ R, then x + iy is a non-real complex number if y ≠ 0.

Explanation:

x + yi is a non-real complex number if y ≠ 0.

If x, y ∈ R.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Complex Numbers and Quadratic Equations - Exercise [पृष्ठ ९६]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 5 Complex Numbers and Quadratic Equations
Exercise | Q 43 | पृष्ठ ९६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`


If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.


Find the value of i + i2 + i3 + i4 


Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`


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:

`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`


Write the conjugates of the following complex number:

`-sqrt(-5)`


Is (1 + i14 + i18 + i22) a real number? Justify your answer


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

`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "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 :


Select the correct answer from the given alternatives:

The value of is `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)` is equal to:


Answer the following:

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

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


Answer the following:

Evaluate: i131 + i49 


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


Answer the following:

show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2


Answer the following:

Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number


Answer the following:

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


Answer the following:

Simplify: `("i"^65 + 1/"i"^145)`


If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| 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)`


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 argument of the complex number z = `(1 + i sqrt(3))(1 + i)(cos theta + i sin theta)` is `(7pi)/12 + theta`.


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.


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 ______.


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


If z = x + iy, then show that `z  barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.


If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.


Multiplicative inverse of 1 + i is ______.


If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.


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


If a + ib = c + id, then ______.


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 ______.


The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.


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


If z = 2 + i, then (z − 1) `(barz − 5) + (barz − 1)` (z − 5) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×