Advertisements
Advertisements
प्रश्न
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"))`
उत्तर
`((2 + "i"))/((3 - "i")(1 + 2"i")) = (2 + "i")/(3 + 6"i" - "i" - 2"i"^2)`
= `(2 + "i")/(3 + 5"i" - 2(-1)` ...[∵ i2 = – 1]
= `(2 + "i")/(5 + 5"i")`
= `(2 + "i")/(5(1 + "i")) = ((2 + "i")(1 - "i"))/(5(1 + "i
")(1 - "i")`
= `(2 - 2"i" + "i" - "i"^2)/(5(1 - "i"^2)`
= `(2 - "i" - (-1))/(5[1 - (-1)]` ...[∵ i2 = – 1]
= `(3 - "i")/10`
∴ `(2 + "i")/((3 - "i")(1 + 2"i")) = 3/10 - 1/10"i"`
∴ a = `3/10 and "b" = (-1)/10`.
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: 5i
Write the conjugates of the following complex numbers: `sqrt(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))`
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)
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20.
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+ 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.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
