Advertisements
Advertisements
Question
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
Advertisements
Solution
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
= `((i + 2))/i*((3i + 4))/i*1/(5 + i)`
= `(3i^2 + 4i + 6i + 8)/(i^2(5 + i)`
= `(-3 + 10i + 8)/(-1(5 + i)` ...[โต i2 = – 1]
= `((5 + 10i))/(-(5 + i))`
= `((5 + 10i)(5 - i))/(-(5 + i)(5 - i)`
= `(25 - 5i + 50i - 10i^2)/(-(25 - i^2)`
= `(25+ 45i -10(-1))/(-[25 -(-1)]`
= `(35 +45i)/(-26)`
= `(-35)/26 - 45/26 i`
APPEARS IN
RELATED QUESTIONS
If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1
Answer the following:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Answer the following:
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Answer the following:
Simplify: `("i"^65 + 1/"i"^145)`
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
Multiplicative inverse of 1 + i is ______.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
