हिंदी

Simplify : -16+3-25+-36--625 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

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

`= sqrt(16 xx -1) + 3sqrt(25 xx - 1) + sqrt(36 xx -1) - sqrt(625 xx -1)`

= 4i + 3(5i) + 6i – 25i

= 4i + 15i + 6i – 25i

= (4 + 15 + 6 – 25)i

= 0i

= 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Complex Numbers - Exercise 1.1 [पृष्ठ ५]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 1 Complex Numbers
Exercise 1.1 | Q 1. (i) | पृष्ठ ५

संबंधित प्रश्न

Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`


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


Evaluate the following:

i457


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


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:

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


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:

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


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


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


Evaluate the following:

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


Write (i25)3 in polar form.


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


Find the principal argument of \[\left( 1 + i\sqrt{3} \right)^2\] .


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


Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.


If i2 = −1, then the sum i + i2 + i3 +... upto 1000 terms is equal to


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


The least positive integer n such that \[\left( \frac{2i}{1 + i} \right)^n\] is a positive integer, is.

 

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


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


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


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


If z is a complex numberthen


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

 


Simplify : `4sqrt(-4) + 5sqrt(-9) - 3sqrt(-16)`


Find a and b if abi = 3a − b + 12i


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:

`((2 + "i"))/((3 - "i")(1 + 2"i"))`


Evaluate the following : i116 


Evaluate the following : i–888 


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


State True or False for the following:

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


The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.


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×