Advertisements
Advertisements
Question
Simplify the following and express in the form a + ib:
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Advertisements
Solution
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
= `(3(i^4*i) + 2(i^4*i^3) + (i^4)^2*i)/(i^4*i^2 + 2(i^4)^2+ 3(i^2)^9)`
= `(3(1)* i + 2(1)(- i) + (1)^2 * i)/((1)(-1) + 2(1)^2 + 3(-1)^9)` ...[∵ i2 = –1, i3 = – i, i4 = 1]
= `(3i - 2i + i)/(-1 + 2 - 3)`
= `(2i)/(-2)`
= – i
APPEARS IN
RELATED QUESTIONS
Find the value of i + i2 + i3 + i4
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"`
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Find the value of x and y which satisfy the following equation (x, y ∈ R).
`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
Answer the following:
Evaluate: i131 + i49
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
Evaluate: (1 + i)6 + (1 – i)3
What is the principal value of amplitude of 1 – i?
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.
If a + ib = c + id, then ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
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 + sqrt3i)^3` is a real number.
