हिंदी

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 :

Advertisements
Advertisements

प्रश्न

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 :

विकल्प

  • −4i

  • 0

  • 4i

  • 4

MCQ
Advertisements

उत्तर

0

Explanation;

1 + (i2)n + (i4)n + (i2)3n

= 1 – 1 + 1 – 1   …(n odd positive interger)

= 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Complex Numbers - Miscellaneous Exercise 1.1 [पृष्ठ २१]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 1 Complex Numbers
Miscellaneous Exercise 1.1 | Q I. (1) | पृष्ठ २१

संबंधित प्रश्न

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

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


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


If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.


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

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


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

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


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:

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


Write the conjugates of the following complex number:

`sqrt(5) - "i"`


Find the value of i + i2 + i3 + i4 


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:

`3 + sqrt(-64)`


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:

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


Solve the following equation for x, y ∈ R:

2x + i9y (2 + i) = xi7 + 10i16


Answer the following:

Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i


Answer the following:

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


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)`


The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.


What is the reciprocal of `3 + sqrt(7)i`.


What is the principal value of amplitude of 1 – i?


If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.


For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"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.


Solve the equation |z| = z + 1 + 2i.


For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.


Multiplicative inverse of 1 + i is ______.


If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.


State True or False for the following:

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


If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.


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


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


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.

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