Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
Advertisements
рдЙрддреНрддрд░
`(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)` ...[тИ╡ 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
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Find the multiplicative inverse of the complex number:
4 – 3i
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0
Answer the following:
Evaluate: i131 + i49
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = `|1/z_1 + 1/z_2 + 1/z_3|` = 1, then |z1 + z2 + z3| is ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Show that `(-1 + sqrt3 i)^3` is a real number.
Evaluate the following:
i35
Show that `(-1 + sqrt3i)^3` is a real number.
