हिंदी

Answer the following: Simplify: i29+i39+i49i30+i40+i50 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Answer the following:

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

योग

उत्तर

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

= `("i"^29(1 + "i"^10 + "i"^20))/("i"^30(1 + "i"^10 + "i"^20)`

= `1/"i" = 1/"i" xx "i"/"i" = "i"/"i"^2`

= `"i"/(-1)`

= – i.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Complex Numbers - Miscellaneous Exercise 1.2 [पृष्ठ २२]

APPEARS IN

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

संबंधित प्रश्न

Find the multiplicative inverse of the complex number.

–i 


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


Show that 1 + i10 + i20 + i30 is a real number.


Find the value of i + i2 + i3 + i4 


Find the value of: x3 –  x2 + x + 46, if x = 2 + 3i


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 – 3x2 + 19x – 20, if x = 1 – 4i


Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`


If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)


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


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:

`3 + sqrt(-64)`


Answer the following:

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

(2 + 3i)(1 − 4i)


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)`


Answer the following:

Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i


Answer the following:

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


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


If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_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 points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.


The equation |z + 1 – i| = |z – 1 + i| represents a ______.


Number of solutions of the equation z2 + |z|2 = 0 is ______.


If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.


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


The value of `sqrt(-25) xx sqrt(-9)` is ______.


The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.


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


The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.


If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) is equal to ______.


Let |z| = |z – 3| = |z – 4i|, then the value |2z| 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 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)`


Find the value of `sqrt(-3) xx sqrt(-6)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×