Advertisements
Advertisements
Question
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)`
Advertisements
Solution
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^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]
= `(3"i" - 2"i" + "i")/(-1 + 2 - 3)`
= `(2"i")/(-2)`
= – i
APPEARS IN
RELATED QUESTIONS
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "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:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
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:
`5/2"i"(-4 - 3"i")`
Answer the following:
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
Number of solutions of the equation z2 + |z|2 = 0 is ______.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| 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.
`(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)`
