Advertisements
Advertisements
Question
If z = x + iy, find the following in rectangular form:
`"Im"(3z + 4bar(z) - 4"i")`
Solution
= Im (3(x + iy) + 4(x – iy) – 4i)
= Im (3x + 3iy + 4x – 4iy – 4i)
= Im (3x + 4 + i(3y – 4y – 4)
= Im (3x + 4x + i(– y – 4))
= Im [7x + i(– y – 4)]
= – y – 4
= – (y + 4)
APPEARS IN
RELATED QUESTIONS
Write the following in the rectangular form:
`bar((5 + 9"i") + (2 - 4"i"))`
Write the following in the rectangular form:
`(10 - 5"i")/(6 + 2"i")`
Write the following in the rectangular form:
`bar(3"i") + 1/(2 - "i")`
If z = x + iy, find the following in rectangular form:
`"Re"(1/z)`
If z = x + iy, find the following in rectangular form:
`"Re"("i"barz)`
If z1 = 2 – i and z2 = – 4 + 3i, find the inverse of z1, z2 and `("z"_1)/("z"_2)`
The complex numbers u v, , and w are related by `1/u = 1/v + 1/w`. If v = 3 – 4i and w = 4 + 3i, find u in rectangular form
Prove the following properties:
z is real if and only if z = `bar(z)`
Find the least value of the positive integer n for which `(sqrt(3) + "i")^"n"` real
Find the least value of the positive integer n for which `(sqrt(3) + "i")^"n"` purely imaginary
Show that `(2 + "i"sqrt(3))^10 - (2 - "i" sqrt(3))^10` is purely imaginary
Show that `((19 - 7"i")/(9 + "i"))^12 + ((20 - 5"i")/(7 - 6"i"))^12` is real
Choose the correct alternative:
The conjugate of a complex number is `1/(" - 2)`. Then, the complex number is
