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: i9 + i19


Express the given complex number in the form a + ib: (1 – i)4


Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`


Evaluate the following:

\[i^{37} + \frac{1}{i^{67}}\].


Evaluate the following:

\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]


Evaluate the following:

\[i^{49} + i^{68} + i^{89} + i^{110}\]


Find the value of the following expression:

i + i2 + i3 + i4


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:

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


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

\[\frac{(1 + i)(1 + \sqrt{3}i)}{1 - i}\] .


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

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


Find the real value of x and y, if

\[(x + iy)(2 - 3i) = 4 + i\]


Find the real value of x and y, if `((1+i)x-2i)/(3+i) + ((2-3i)y+i)/(3-i) = i, xy ∈ R, i = sqrt-1`


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

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


Find the least positive integral value of n for which  \[\left( \frac{1 + i}{1 - i} \right)^n\] is real.


If \[\left( \frac{1 + i}{1 - i} \right)^3 - \left( \frac{1 - i}{1 + i} \right)^3 = x + iy\] find (x, y).


If \[\frac{\left( 1 + i \right)^2}{2 - i} = x + iy\]  find x + y.


Evaluate the following:

\[x^4 - 4 x^3 + 4 x^2 + 8x + 44,\text {  when } x = 3 + 2i\]


If \[\left| z + 1 \right| = z + 2\left( 1 + i \right)\],find z.


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


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


If \[\frac{\left( a^2 + 1 \right)^2}{2a - i} = x + iy\] find the value of  \[x^2 + y^2\].


For any two complex numbers z1 and z2 and any two real numbers a, b, find the value of \[\left| a z_1 - b z_2 \right|^2 + \left| a z_2 + b z_1 \right|^2\].


If \[\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}\],find z.


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


If z is a complex number, then


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


Find a and b if (a + ib) (1 + i) = 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)−1 


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`


Show that `(-1 + sqrt(3)"i")^3` is a real number


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


Evaluate the following : i116 


Evaluate the following : i30 + i40 + i50 + i60 


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


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×