Advertisements
Advertisements
Question
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Advertisements
Solution
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
= `((sqrt(5) + sqrt(3)"i")(sqrt(5) + sqrt(3)"i"))/((sqrt(5) - sqrt(3)"i")(sqrt(5) + sqrt(3)"i")`
= `(5 + 2sqrt(15)"i" + 3"i"^2)/(5 - 3"i"^2)`
= `(5 + 2sqrt(15)"i" + 3(-1))/(5 - 3(-1)` ...[∵ i2 = – 1]
= `(2 + 2sqrt(15)"i")/8`
= `(1 + sqrt(15)"i")/4`
= `1/4 + (sqrt(15)"i")/4`.
APPEARS IN
RELATED QUESTIONS
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Find the value of x and y which satisfy the following equation (x, y∈R).
If x(1 + 3i) + y(2 − i) − 5 + i3 = 0, find x + y
Answer the following:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Answer the following:
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
The value of (2 + i)3 × (2 – i)3 is ______.
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` 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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
