Advertisements
Advertisements
प्रश्न
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Advertisements
उत्तर
`(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
संबंधित प्रश्न
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
Simplify the following and express in the form a + ib:
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Write the conjugates of the following complex number:
3 + i
Write the conjugates of the following complex number:
3 – i
Show that 1 + i10 + i100 − i1000 = 0
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
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"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
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)`
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18`
