हिंदी

State True or False for the following: 2 is not a complex number. - Mathematics

Advertisements
Advertisements

प्रश्न

State True or False for the following:

2 is not a complex number.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is True.

Explanation:

Since 2 has no imaginary part.

So, 2 is not a complex number.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Complex Numbers and Quadratic Equations - Exercise [पृष्ठ ९३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 5 Complex Numbers and Quadratic Equations
Exercise | Q 26.(viii) | पृष्ठ ९३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`


Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`


Evaluate the following:

(ii) i528


Evaluate the following:

 \[\frac{1}{i^{58}}\]


Evaluate the following:

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


Evaluate the following:

 \[i^{30} + i^{40} + i^{60}\]


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


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

\[(1 + i)(1 + 2i)\]


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

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


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


Evaluate the following:

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


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


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


If π < θ < 2π and z = 1 + cos θ + i sin θ, then write the value of \[\left| z \right|\] .


Write 1 − i in polar form.


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


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


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 polar form of (i25)3 is


If a = cos θ + i sin θ, then \[\frac{1 + a}{1 - a} =\]


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 


If \[z = a + ib\]  lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if


Which of the following is correct for any two complex numbers z1 and z2?

 


Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`


Find a and b if (a – b) + (a + b)i = a + 5i


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


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:

`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"i")`


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

`(2 + sqrt(-3))/(4 + sqrt(-3))`


Evaluate the following : i93  


Evaluate the following : i–888 


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


Match the statements of Column A and Column B.

Column A Column B
(a) The polar form of `i + sqrt(3)` is  (i) Perpendicular bisector of
segment joining (–2, 0)
and (2, 0).
(b) The amplitude of `-1 + sqrt(-3)` is  (ii) On or outside the circle
having centre at (0, –4)
and radius 3.
(c) If |z + 2| = |z − 2|, then locus of z is (iii) `(2pi)/3`
(d) If |z + 2i| = |z − 2i|, then locus of z is (iv) Perpendicular bisector of
segment joining (0, –2) and (0, 2).
(e) Region represented by |z + 4i| ≥ 3 is  (v) `2(cos  pi/6 + i sin  pi/6)`
(f) Region represented by |z + 4| ≤ 3 is  (vi) On or inside the circle having
centre (–4, 0) and radius 3 units.
(g) Conjugate of `(1 + 2i)/(1 - i)` lies in (vii) First quadrant
(h) Reciprocal of 1 – i lies in (viii) Third quadrant

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


Show that `(-1+sqrt3i)^3` is a real number.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×