हिंदी

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6) - Mathematics

Advertisements
Advertisements

प्रश्न

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

योग

उत्तर

(1 – i) – (-1 + i6) = (1 – i) + (1 – 6i)

= 1 – i + 1 – 6i

= 2 – 7i

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Complex Numbers and Quadratic Equations - Exercise 5.1 [पृष्ठ १०४]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 5 Complex Numbers and Quadratic Equations
Exercise 5.1 | Q 5 | पृष्ठ १०४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Express the given complex number in the form a + ib: i9 + i19


Evaluate the following:

(ii) i528


Evaluate the following:

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


Find the value of the following expression:

\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]


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:

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


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

\[\frac{(1 + i)x - 2i}{3 + i} + \frac{(2 - 3i)y + i}{3 - i}\]


Find the multiplicative inverse of the following complex number:

1 − i


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


Evaluate the following:

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


Evaluate the following:

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


For a positive integer n, find the value of \[(1 - i )^n \left( 1 - \frac{1}{i} \right)^n\].


If \[\frac{z - 1}{z + 1}\] is purely imaginary number (\[z \neq - 1\]), find the value of \[\left| z \right|\].


If z1z2z3 are complex numbers such that \[\left| z_1 \right| = \left| z_2 \right| = \left| z_3 \right| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1\] then find the value of \[\left| z_1 + z_2 + z_3 \right|\] .


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

\[\frac{1 - i}{\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}}\]


If n is any positive integer, write the value of \[\frac{i^{4n + 1} - i^{4n - 1}}{2}\].


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


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


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.


If `(3+2i sintheta)/(1-2 i sin theta)`is a real number and 0 < θ < 2π, then θ =


\[(\sqrt{- 2})(\sqrt{- 3})\] is equal to


If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals


If \[z = \frac{1 + 2i}{1 - (1 - i )^2}\], then arg (z) equal


If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =


If \[x + iy = \frac{3 + 5i}{7 - 6i},\]  then y =


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


The value of \[(1 + i )^4 + (1 - i )^4\] is


If z is a complex numberthen


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:

`("i"(4 + 3"i"))/((1 - "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`


Evaluate the following : i403 


Answer the following:

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


If a = cosθ + isinθ, find the value of `(1 + "a")/(1 - "a")`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×