मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Answer the following: Simplify: (i65+1i145)

Advertisements
Advertisements

प्रश्न

Answer the following:

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

बेरीज
Advertisements

उत्तर

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

= `|("i"^4)^16*"i" + 1/(("i"^4)^36*"i")|`

= `"i" + 1/"i"`

= `("i"^2 + 1)/"i"`

= `(-1 + 1)/"i"`

= 0

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Complex Numbers - Miscellaneous Exercise 1.2 [पृष्ठ २२]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 1 Complex Numbers
Miscellaneous Exercise 1.2 | Q II. (16) (ii) | पृष्ठ २२

संबंधित प्रश्‍न

Find the multiplicative inverse of the complex number:

4 – 3i


Find the number of non-zero integral solutions of the equation `|1-i|^x  = 2^x`.


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

(2 + 3i)(1 – 4i)


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")`


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")`


Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.


Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i


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

`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = 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:

`sqrt(-3) sqrt(-6)` is equal to


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:

(2 + 3i)(1 − 4i)


Answer the following:

Evaluate: (1 − i + i2)−15 


Answer the following:

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


Answer the following:

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


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


The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______


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


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


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 ______.


State true or false for the following:

The complex number cosθ + isinθ can be zero for some θ.


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 n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.


What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?


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


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.


The value of `(z + 3)(barz + 3)` is equivalent to ______.


The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.


If z is a complex number, then ______.


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 a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| 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)`


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

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


i2 + i3 + ... + i4000 =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×