हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

`(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
  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 6 | पृष्ठ १०४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a2 + b= `(x^2 + 1)^2/(2x + 1)^2`


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


Evaluate the following:

(ii) i528


Evaluate the following:

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


Find the value of the following expression:

i + i2 + i3 + i4


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

\[\frac{3 + 2i}{- 2 + i}\]


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

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


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

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


Find the multiplicative inverse of the following complex number:

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


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


Evaluate the following:

\[x^4 + 4 x^3 + 6 x^2 + 4x + 9, \text { when } x = - 1 + i\sqrt{2}\]


Solve the system of equations \[\text { Re }\left( z^2 \right) = 0, \left| z \right| = 2\].


If z1 is a complex number other than −1 such that \[\left| z_1 \right| = 1\] and \[z_2 = \frac{z_1 - 1}{z_1 + 1}\] then show that the real parts of z2 is zero.


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


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


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


If z1 and z2 are two complex numbers such that \[\left| z_1 \right| = \left| z_2 \right|\] and arg(z1) + arg(z2) = \[\pi\] then show that \[z_1 = - \bar{{z_2}}\].


Express \[\sin\frac{\pi}{5} + i\left( 1 - \cos\frac{\pi}{5} \right)\] in polar form.


If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.


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


The amplitude of \[\frac{1}{i}\] is equal to


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


If z is a complex numberthen


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:

`("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`


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

(1 + i)−3 


Evaluate the following : i35 


Evaluate the following : i116 


Evaluate the following : i403 


If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.


State true or false for the following:

If a complex number coincides with its conjugate, then the number must lie on imaginary axis.


Match the statements of column A and B.

Column A Column B
(a) The value of 1 + i2 + i4 + i6 + ... i20 is (i) purely imaginary complex number
(b) The value of `i^(-1097)` is (ii) purely real complex number
(c) Conjugate of 1 + i lies in (iii) second quadrant
(d) `(1 + 2i)/(1 - i)` lies in (iv) Fourth quadrant
(e) If a, b, c ∈ R and b2 – 4ac < 0, then
the roots of the equation ax2 + bx + c = 0
are non real (complex) and
(v) may not occur in conjugate pairs
(f) If a, b, c ∈ R and b2 – 4ac > 0, and
b2 – 4ac is a perfect square, then the
roots of the equation ax2 + bx + c = 0
(vi) may occur in conjugate pairs

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

(w2 + w − 1)3 = −8


Find the value of `(i^(592) + i^(590) + i^(588) + i^(586) + i^(584))/(i^(582) + i^(580) + i^(578) + i^(576) + i^(574))`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×