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

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: `(5i) (- 3/5 i)`


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


Evaluate the following:

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


Find the value of the following expression:

i5 + i10 + i15


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 real value of x and y, if

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


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

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


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


If \[\left( \frac{1 - i}{1 + i} \right)^{100} = a + ib\] find (a, b).


Evaluate the following:

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


Evaluate the following:

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


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):

1 − sin α + i cos α


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


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


If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to


If \[z = \frac{1 + 7i}{(2 - i )^2}\] , then


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?

 


Find a and b if abi = 3a − b + 12i


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 


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)


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 


If `((1 + "i"sqrt3)/(1 - "i"sqrt3))^"n"` is an integer, then n is ______.


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:

The order relation is defined on the set of complex numbers.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×