Advertisements
Advertisements
Question
Evaluate the following : i116
Advertisements
Solution
i116 = (i2)58
= (– 1)58
= 1.
APPEARS IN
RELATED QUESTIONS
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Evaluate the following:
i457
Evaluate the following:
\[i^{37} + \frac{1}{i^{67}}\].
Show that 1 + i10 + i20 + i30 is a real number.
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 value of the following expression:
1+ i2 + i4 + i6 + i8 + ... + i20
Find the value of the following expression:
(1 + i)6 + (1 − i)3
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:
\[\frac{2 + 3i}{4 + 5i}\]
Express the following complex number in the standard form a + i b:
\[\frac{5 + \sqrt{2}i}{1 - 2\sqrt{i}}\]
Find the real values of θ for which the complex number \[\frac{1 + i cos\theta}{1 - 2i cos\theta}\] is purely real.
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 \[z = - i \bar{z}\].
Solve the equation \[\left| z \right| = z + 1 + 2i\].
What is the smallest positive integer n for which \[\left( 1 + i \right)^{2n} = \left( 1 - i \right)^{2n}\] ?
Write (i25)3 in polar form.
Express the following complex in the form r(cos θ + i sin θ):
\[\frac{1 - i}{\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}}\]
Write −1 + i \[\sqrt{3}\] in polar form .
Write the argument of −i.
Write the sum of the series \[i + i^2 + i^3 + . . . .\] upto 1000 terms.
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
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 (x + iy)1/3 = a + ib, then \[\frac{x}{a} + \frac{y}{b} =\]
If \[z = \frac{1 + 2i}{1 - (1 - i )^2}\], then arg (z) equal
The amplitude of \[\frac{1 + i\sqrt{3}}{\sqrt{3} + i}\] is
\[\frac{1 + 2i + 3 i^2}{1 - 2i + 3 i^2}\] equals
If \[z = a + ib\] lies in third quadrant, then \[\frac{\bar{z}}{z}\] also lies in third quadrant if
The complex number z which satisfies the condition \[\left| \frac{i + z}{i - z} \right| = 1\] lies on
Which of the following is correct for any two complex numbers z1 and z2?
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"))`
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"))^2`
Show that `(-1 + sqrt(3)"i")^3` is a real number
If z1 and z2 both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.
The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.
Show that `(-1+ sqrt(3)i)^3` is a real number.
