Question

For each of the following complex numbers give the, absolute value; the opposite; the conjugate:
1) 3-4i
2) 8i

Answer 1

the absolute value is the length of the complex number when we think of it as a vector:
eg 2 + 6i


we use Pythagoras' theorem

\[|2 + 6i| = \sqrt{2^2 + 6^2} = \sqrt{40}\]

the conjugate is the same complex number z, but we change the sign of the imaginary part, common notation is z* is the conjugate of z

for z = 2 + 6i

z* = 2 -6i

when you say opposite do you inverse?