हिंदी

Answer the following: Simplify the following and express in the form a + ib: 52i(-4-3i)

Advertisements
Advertisements

प्रश्न

Answer the following:

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

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

योग
Advertisements

उत्तर

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

= `-10"i" - 15/2"i"^2`

= `-10"i" + 15/2`   ...[∵ i2 = – 1]

= `15/2 - 10"i"`, which is of the form a + bi.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Complex Numbers - Miscellaneous Exercise 1.2 [पृष्ठ २१]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
अध्याय 1 Complex Numbers
Miscellaneous Exercise 1.2 | Q II. (1) (iv) | पृष्ठ २१

संबंधित प्रश्न

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


Find the value of i49 + i68 + i89 + i110 


Find the value of i + i2 + i3 + i4 


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

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


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


Evaluate: `("i"^37 + 1/"i"^67)`


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).

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


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:

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

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


Answer the following:

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


If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.


Evaluate: (1 + i)6 + (1 – i)3 


If z1, z2, z3 are complex numbers such that `|z_1| = |z_2| = |z_3| = |1/z_1 + 1/z_2 + 1/z_3|` = 1, then find the value of |z1 + z2 + z3|.


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 ______.


The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.


What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?


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


What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?


If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).


If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.


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


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


State True or False for the following:

The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).


Which of the following is correct for any two complex numbers z1 and z2?


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


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


If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.


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)`


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.


i2 + i3 + ... + i4000 =


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×