Advertisements
Advertisements
प्रश्न
Answer the following:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Advertisements
उत्तर
`3 + sqrt(-64) = 3 + sqrt(64)*sqrt(-1)`
= 3 + 8i
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
–i
If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(2i3)2
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Write the conjugates of the following complex number:
`-sqrt(-5)`
Write the conjugates of the following complex number:
5i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Write the conjugates of the following complex number:
cosθ + i sinθ
If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Answer the following:
Simplify the following and express in the form a + ib:
(2i3)2
Answer the following:
Simplify the following and express in the form a + ib:
(1 + 3i)2(3 + i)
Answer the following:
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
Locate the points for which 3 < |z| < 4.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.
If |z + 1| = z + 2(1 + i), then find z.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
State True or False for the following:
The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| is equal to ______.
If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.
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)`
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
