Advertisements
Advertisements
Question
Answer the following:
Evaluate: i131 + i49
Solution
i131 + i49
= i130.i + i48.i
= (i2)65.i + (i2)24.i
= (– 1)65.i + (– 1)24.i
= – i + i
= 0.
APPEARS IN
RELATED QUESTIONS
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Find the value of i49 + i68 + i89 + i110
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
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)`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Write the conjugates of the following complex number:
`-sqrt(5) - sqrt(7)"i"`
If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
Answer the following:
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
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)`
Answer the following:
Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
Locate the points for which 3 < |z| < 4.
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
State true or false for the following:
The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.
State true or false for the following:
If three complex numbers z1, z2 and z3 are in A.P., then they lie on a circle in the complex plane.
Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.
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.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
Which of the following is correct for any two complex numbers z1 and z2?
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
Find the value of `(i^592 + i^590 + i^588 + i^586 + i^584)/ (i^582 + i^580 + i^578 + i^576 + i^574)`
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)`
Evaluate the following:
i35
Show that `(-1 + sqrt3i)^3` is a real number.
