English

Express the given complex number in the form a + ib: (15+i25)-(4+i52)

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

`(1/5 + i2/5) - (4 + i 5/2 )`

= `1/5 + 2/5 i-4 - 5/2i`

= `(-4+1/5) + (2/5-5/2)i`

= `((1 - 20)/5) + i ((4 - 25)/10)`

= `(-19)/5 + (4 - 25)/10 i`

= `(-19)/5 + (-21)/10i`

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 6. | Page 83

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Express the given complex number in the form a + ib: i–39


Evaluate: `[i^18 + (1/i)^25]^3`


Evaluate the following:

 \[i^{30} + i^{40} + i^{60}\]


Find the value of the following expression:

i49 + i68 + i89 + i110


Find the value of the following expression:

i + i2 + i3 + i4


Find the value of the following expression:

i5 + i10 + i15


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 + ib:

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


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

\[\frac{2 + 3i}{4 + 5i}\]


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

\[(1 + 2i )^{- 3}\]


Find the real value of x and y, if

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


Find the multiplicative inverse of the following complex number:

1 − i


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

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


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

Im `(1/(z_1overlinez_1))`


Find the real values of θ for which the complex number \[\frac{1 + i cos\theta}{1 - 2i cos\theta}\]  is purely real.


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


Evaluate the following:

\[2 x^4 + 5 x^3 + 7 x^2 - x + 41, \text { when } x = - 2 - \sqrt{3}i\]


If \[\left( 1 + i \right)z = \left( 1 - i \right) \bar{z}\],then show that \[z = - i \bar{z}\].


Solve the equation \[\left| z \right| = z + 1 + 2i\].


Write (i25)3 in polar form.


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


Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.


Write the argument of \[\left( 1 + i\sqrt{3} \right)\left( 1 + i \right)\left( \cos\theta + i\sin\theta \right)\].

Disclaimer: There is a misprinting in the question. It should be  \[\left( 1 + i\sqrt{3} \right)\]  instead of \[\left( 1 + \sqrt{3} \right)\].


If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to


If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]


If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =


\[\frac{1 + 2i + 3 i^2}{1 - 2i + 3 i^2}\] equals


The value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1\] is 


If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on


Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i


Find a and b if abi = 3a − b + 12i


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"))`


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"))^2`


Find the value of `(3 + 2/i) (i^6 - i^7) (1 + i^11)`.


Answer the following:

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


State True or False for the following:

The order relation is defined on the set of complex numbers.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×