English

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Advertisements
Advertisements

Question

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Sum
Advertisements

Solution

3(7 + i7) + i (7 + i7)

= 21 + 21i + 7i + 7i2

= 21 + 28i + 7(-1)   [∵ i2 = -1]

= 21 – 7 + 28i

= 14 + 28i

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Complex Numbers and Quadratic Equations - EXERCISE 4.1 [Page 83]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 4 Complex Numbers and Quadratic Equations
EXERCISE 4.1 | Q 4. | Page 83

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`


Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`


Evaluate the following:

i457


Find the value of the following expression:

1+ i2 + i4 + i6 + i8 + ... + i20


Express the following complex number in the standard form a + i b:

\[\frac{1}{(2 + i )^2}\]


Express the following complex number in the standard form a + i b:

\[(1 + i)(1 + 2i)\]


Express the following complex number in the standard form a + i b:

\[\frac{1 - i}{1 + i}\]


Express the following complex number in the standard form a + ib:

\[\frac{(2 + i )^3}{2 + 3i}\]


Express the following complex number in the standard form a + i b:

\[\frac{(1 - i )^3}{1 - i^3}\]


Find the real value of x and y, if

\[(3x - 2iy)(2 + i )^2 = 10(1 + i)\]


Find the real value of x and y, if

\[(1 + i)(x + iy) = 2 - 5i\]


If \[z_1 = 2 - i, z_2 = 1 + i,\text {  find } \left| \frac{z_1 + z_2 + 1}{z_1 - z_2 + i} \right|\]


If \[z_1 = 2 - i, z_2 = - 2 + i,\] find 

Re \[\left( \frac{z_1 z_2}{z_1} \right)\]


If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.


If \[a = \cos\theta + i\sin\theta\], find the value of \[\frac{1 + a}{1 - a}\].


Evaluate the following:

\[2 x^3 + 2 x^2 - 7x + 72, \text { when } x = \frac{3 - 5i}{2}\]


Evaluate the following:

\[x^6 + x^4 + x^2 + 1, \text { when }x = \frac{1 + i}{\sqrt{2}}\]


What is the smallest positive integer n for which \[\left( 1 + i \right)^{2n} = \left( 1 - i \right)^{2n}\] ?


Express the following complex in the form r(cos θ + i sin θ):
1 + i tan α


Write the argument of −i.


Find z, if \[\left| z \right| = 4 \text { and }\arg(z) = \frac{5\pi}{6} .\]


Write the value of \[\sqrt{- 25} \times \sqrt{- 9}\].


Write the sum of the series \[i + i^2 + i^3 + . . . .\] upto 1000 terms.


If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].


The value of \[(1 + i)(1 + i^2 )(1 + i^3 )(1 + i^4 )\] is.


The amplitude of \[\frac{1 + i\sqrt{3}}{\sqrt{3} + i}\] is 


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

 


Find a and b if abi = 3a − b + 12i


Find a and b if `1/("a" + "ib")` = 3 – 2i


Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:

(1 + i)(1 − i)−1 


Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:

`((2 + "i"))/((3 - "i")(1 + 2"i"))`


Evaluate the following : i93  


Evaluate the following : i116 


Answer the following:

Show that z = `5/((1 - "i")(2 - "i")(3 - "i"))` is purely imaginary number.


If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).


If w is a complex cube-root of unity, then prove the following

(w2 + w − 1)3 = −8


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×