Advertisements
Advertisements
प्रश्न
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20.
उत्तर
1 + i2 + i4 + i6 + i8 + ... + i20
= 1 + (i2 + i4) + (i6 + i8) + (i10 + i12) + (i14 + i16) + (i18 + i20)
= 1 + [i2 + (i2)2] + [(i2)3 + (i2)4] + [(i2)5 + (i2)6] + [(i2)7 + (i2)8] + [(i2)9 + (i2)10]
= 1 + [– 1 + ( – 1)2] + [(– 1)3 + (– 1)4] + [(– 1)5 + (– 1)6] + [(– 1)7 + (– 1)8] + [(– 1)9 + (– 1)10] ...[∵ i2 = – 1]
= 1 + (– 1 + 1) + (– 1 + 1) + (– 1 + 1) + (– 1 + 1) + (– 1 + 1)
= 1 + 0 + 0 + 0 + 0 + 0
= 1.
APPEARS IN
संबंधित प्रश्न
Write the conjugates of the following complex numbers: 3 + i
Write the conjugates of the following complex numbers: 3 – i
Write the conjugates of the following complex numbers: `-sqrt(5) - sqrt(7) "i"`
Write the conjugates of the following complex numbers: 5i
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: `(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: `(2 + sqrt(-3))/(4 + sqrt(-3))`
Show that `(-1 + sqrt(3) i)^3` is a real number.
Show that `(−1 + sqrt3 i)^3` is a real number.
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Show that `(−1+ sqrt3 i)^3` is a real number.
Show that `(−1 + sqrt(3) i)^3` is a real number.
Show that `(-1 + sqrt3"i")^3` is a real number.
Show that `(-1 + sqrt3i)^3` is a real number.
Show that `(- 1 + sqrt3 i)^3` is a real number.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
