Advertisements
Advertisements
प्रश्न
Express the given complex number in the form a + ib: i9 + i19
Advertisements
उत्तर
i9 + i19 = i8.i + i18.i.
= [i2]4.i + [i2]9. i
= (-1)4 i + (-1)9 i
= i + (-1)i
= i – i = 0
= 0 + 0i
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib: i–39
Express the given complex number in the form a + ib:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Evaluate the following:
(ii) i528
Evaluate the following:
\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]
Evaluate the following:
\[i^{30} + i^{40} + i^{60}\]
Express the following complex number in the standard form a + i b:
\[(1 + 2i )^{- 3}\]
Express the following complex number in the standard form a + i b:
\[\frac{3 - 4i}{(4 - 2i)(1 + i)}\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Re \[\left( \frac{z_1 z_2}{z_1} \right)\]
If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.
Find the smallest positive integer value of m for which \[\frac{(1 + i )^n}{(1 - i )^{n - 2}}\] is a real number.
Evaluate the following:
\[x^4 - 4 x^3 + 4 x^2 + 8x + 44,\text { when } x = 3 + 2i\]
Evaluate the following:
\[x^6 + x^4 + x^2 + 1, \text { when }x = \frac{1 + i}{\sqrt{2}}\]
If \[\frac{z - 1}{z + 1}\] is purely imaginary number (\[z \neq - 1\]), find the value of \[\left| z \right|\].
Express \[\sin\frac{\pi}{5} + i\left( 1 - \cos\frac{\pi}{5} \right)\] in polar form.
Write 1 − i in polar form.
Write −1 + i \[\sqrt{3}\] in polar form .
Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].
If \[\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}\],find z.
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 \[\left( 1 + \sqrt{3} \right)\].
If `(3+2i sintheta)/(1-2 i sin theta)`is a real number and 0 < θ < 2π, then θ =
The least positive integer n such that \[\left( \frac{2i}{1 + i} \right)^n\] is a positive integer, is.
\[\text { If } z = \frac{1}{(2 + 3i )^2}, \text { than } \left| z \right| =\]
If \[x + iy = \frac{3 + 5i}{7 - 6i},\] then y =
If \[z = \frac{1 + 7i}{(2 - i )^2}\] , then
The amplitude of \[\frac{1}{i}\] is equal to
The amplitude of \[\frac{1 + i\sqrt{3}}{\sqrt{3} + i}\] is
\[\frac{1 + 2i + 3 i^2}{1 - 2i + 3 i^2}\] equals
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"))`
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
Evaluate the following : i–888
The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.
