Advertisements
Advertisements
Question
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Advertisements
Solution
`5/2"i"(- 4 - 3 "i")`
= `5/2(- 4"i" - 3 "i"^2)`
= `5/2[-4"i" - 3(-1)]` ...[∵ i2 = – 1]
= `5/2(3 - 4"i")`
= `15/2 - 10"i"`
APPEARS IN
RELATED QUESTIONS
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Write the conjugates of the following complex number:
cosθ + i sinθ
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)
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
Find the value of k if for the complex numbers z1 and z2, `|1 - barz_1z_2|^2 - |z_1 - z_2|^2 = k(1 - |z_1|^2)(1 - |"z"_2|^2)`
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real 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`.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
Which of the following is correct for any two complex numbers z1 and z2?
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
