Advertisements
Advertisements
Question
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Advertisements
Solution
`(4 + 3"i")/(1 - "i") = ((4 + 3"i")(1 + "i"))/((1 - "i")(1 + "i")`
= `(4 + 4"i" + 3"i" + 3"i"^2)/(1 - "i"^2)`
= `(4 + 7"i" + 3(-1))/(1 - (-1)` ...[∵ i2 = – 1]
= `(1 + 7"i")/2`
= `1/2+7/2"i"`.
APPEARS IN
RELATED QUESTIONS
Find the multiplicative inverse of the complex number:
4 – 3i
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Write the conjugates of the following complex number:
5i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Show that 1 + i10 + i100 − i1000 = 0
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
Answer the following:
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Answer the following:
Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i
Answer the following:
Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i
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 ______
State true or false for the following:
The argument of the complex number z = `(1 + i sqrt(3))(1 + i)(cos theta + i sin theta)` is `(7pi)/12 + theta`.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
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)`
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)`
