मराठी

State true or false for the following: If a complex number coincides with its conjugate, then the number must lie on imaginary axis.

Advertisements
Advertisements

प्रश्न

State true or false for the following:

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

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

This statement is False.

Explanation:

Because x + iy = x – iy

⇒ y = 0

⇒ number lies on x-axis.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Complex Numbers and Quadratic Equations - Solved Examples [पृष्ठ ८५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 17.(iii) | पृष्ठ ८५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`


Evaluate the following:

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


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 + ib:

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


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:

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


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

\[\frac{3 - 4i}{(4 - 2i)(1 + i)}\]


Find the real value of x and y, if

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


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


Evaluate the following:

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


Evaluate the following:

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


Evaluate the following:

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


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


Find the number of solutions of \[z^2 + \left| z \right|^2 = 0\].


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


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

 tan α − i


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


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


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 \[\left( 1 + \sqrt{3} \right)\].


The principal value of the amplitude of (1 + i) is


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


\[\text { If  }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]


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


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 


The complex number z which satisfies the condition \[\left| \frac{i + z}{i - z} \right| = 1\] lies on


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 + 2i)(– 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:

(2 + 3i)(2 – 3i)


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

`(4"i"^8 - 3"i"^9 + 3)/(3"i"^11 - 4"i"^10 - 2)`


Evaluate the following : i35 


Evaluate the following : i888 


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

State True or False for the following:

2 is not a complex number.


Show that `(-1 + sqrt3 "i")^3` is a real number.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×