Advertisements
Advertisements
प्रश्न
Find the value of i49 + i68 + i89 + i110
उत्तर
i49 + i68 + i89 + i110
= (i4)12 .i + (i4)17 + (i4)22 .i + (i4)27 .i2
= (1)12 .i + (1)17 + (1)22 .i + (1)27 (– 1) ...[∵ i4 = 1, i2 = – 1]
= i + 1 + i – 1
= 2i
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
–i
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Write the conjugates of the following complex number:
3 + i
Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
Find the value of k if for the complex numbers z1 and z2, `|1 - barz_1z_2|^2 - |z_1 - z_2|^2 = k(1 - |z_1|^2)(1 - |"z"_2|^2)`
1 + i2 + i4 + i6 + ... + i2n is ______.
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9) / (i^6 + 2i^8 + 3i^18)`
Evaluate the following:
i35