Advertisements
Advertisements
Question
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")`
Solution
`(3 + 2"i")/(2 - 5"i") + (3 - 2"i")/(2 + 5"i")`
= `((3 + 2"i")(2 + 5"i") + (2 - 5"i")(3 - 2"i"))/((2 - 5"i")(2 + 5"i"))`
= `(6 + 15"i" + 4"i" + 10"i"^2 + 6 - 4"i" - 15"i" + 10"i"^2)/(4 - 25"i"^2)`
= `(12 + 20"i"^2)/(4 - 25"i"^2)`
= `(12 + 20(-1))/(4 - 25(-1))` ...[∵ i2 = – 1]
= `(-8)/(29)`
∴ `(3 + 2"i")/(2 - 5"i") + (3 - 2"i")/(2 + 5"i") = (-8)/29 + 0"i"`
∴ a = `(-8)/29 and "b"` = 0
APPEARS IN
RELATED QUESTIONS
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 number:
`-sqrt(-5)`
Write the conjugates of the following complex numbers: 5i
Write the conjugates of the following complex numbers: `sqrt(5) - "i"`
Write the conjugates of the following complex numbers: `sqrt(2) + sqrt(3) "i"`
Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(-1)`. State the values of a and b: `("i"(4 + 3"i"))/((1 - "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: `(4"i"^8 - 3"i"^9 + 3)/(3"i"^11 - 4"i"^10 - 2)`
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20.
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 + 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)`
