English

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

Advertisements
Advertisements

Question

Answer the following:

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

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

Sum

Solution

`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
  Is there an error in this question or solution?
Chapter 1: Complex Numbers - Miscellaneous Exercise 1.2 [Page 21]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
Chapter 1 Complex Numbers
Miscellaneous Exercise 1.2 | Q II. (1) (iv) | Page 21

RELATED QUESTIONS

Find the multiplicative inverse of the complex number.

`sqrt5 + 3i`


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


Find the value of i49 + i68 + i89 + i110 


Find the value of i + i2 + i3 + i4 


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


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:

(2 + 3i)(1 – 4i)


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:

`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`


Write the conjugates of the following complex number:

`sqrt(5) - "i"`


Write the conjugates of the following complex number:

`sqrt(2) + sqrt(3)"i"`


Write the conjugates of the following complex number:

cosθ + i sinθ


Simplify : `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)`


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


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")`


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

If x(1 + 3i) + y(2 − i) − 5 + i3 = 0, 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:

(2 + 3i)(1 − 4i)


Answer the following:

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

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


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:

`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`


Answer the following:

Solve the following equations for x, y ∈ R:

(x + iy) (5 + 6i) = 2 + 3i


Answer the following:

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


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`.


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


Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.


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


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).


If `((1 + i)/(1 - i))^x` = 1, then ______.


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 ______.


Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.


If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = `|1/z_1 + 1/z_2 + 1/z_3|` = 1, then |z1 + z2 + z3| is ______.


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


Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.


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×