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)`
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
Find the multiplicative inverse of the complex number.
–i
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
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 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:
(2 + 3i)(1 − 4i)
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
The value of (2 + i)3 × (2 – i)3 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.
What is the reciprocal of `3 + sqrt(7)i`.
Solve the equation |z| = z + 1 + 2i.
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) 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 ______.
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)`
