Advertisements
Advertisements
Question
Answer the following:
Simplify the following and express in the form a + ib:
(2 + 3i)(1 − 4i)
Advertisements
Solution
(2 + 3i)(1 − 4i) = 2 − 8i + 3i − 12i2
= 2 − 5i − 12(− 1) ...[∵ i2 = − 1]
= 14 − 5i
APPEARS IN
RELATED QUESTIONS
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.
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Find the value of i49 + i68 + i89 + i110
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Evaluate: `("i"^37 + 1/"i"^67)`
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
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:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Answer the following:
Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
Locate the points for which 3 < |z| < 4.
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
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`.
State true or false for the following:
If n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.
1 + i2 + i4 + i6 + ... + i2n is ______.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.
If |z + 1| = z + 2(1 + i), then find z.
Multiplicative inverse of 1 + i is ______.
The real value of α for which the expression `(1 - i sin alpha)/(1 + 2i sin alpha)` is purely real is ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| 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 ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.
Evaluate the following:
i35
