English

Evaluate the following : i888 - Mathematics and Statistics

Advertisements
Advertisements

Question

Evaluate the following : i888 

Sum

Solution

i888 = (i2)444

= (– 1)444

= 1.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Complex Numbers - Exercise 1.1 [Page 6]

RELATED QUESTIONS

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)


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


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


Find the value of the following expression:

i49 + i68 + i89 + i110


Find the value of the following expression:

i30 + i80 + i120


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

\[(x + iy)(2 - 3i) = 4 + i\]


If \[z_1 = 2 - i, z_2 = 1 + i,\text {  find } \left| \frac{z_1 + z_2 + 1}{z_1 - z_2 + i} \right|\]


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

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


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


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


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):

1 − sin α + i cos α


If n is any positive integer, write the value of \[\frac{i^{4n + 1} - i^{4n - 1}}{2}\].


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


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


If \[\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}\],find z.


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

 

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


If (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]


If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals


The value of (i5 + i6 + i7 + i8 + i9) / (1 + i) is


A real value of x satisfies the equation  \[\frac{3 - 4ix}{3 + 4ix} = a - ib (a, b \in \mathbb{R}), if a^2 + b^2 =\]


If z is a complex numberthen


If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on


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


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:

`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`


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)


Evaluate the following : i93  


Evaluate the following : i116 


Evaluate the following : `1/"i"^58`


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


If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).


State True or False for the following:

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


State True or False for the following:

2 is not a complex number.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×