Question

Assign Re(z) and Im(z) for:
z= 3-i/1+i ?

Answer 1

Multiply by the conjugate of the denominator? As in \[
\frac{3-i}{1+i}\times \frac{1-i}{1-i}
\]

Answer 2

It should simplify.

Answer 3

Thank you. So when I find the answer, so I say that the real number (without the Im) is ? and Im is ? Thanks.

Answer 4

It will simplify to \(a+bi\) though \(a\) and \(b\) may be fractions.

Answer 5

The answers are \(Re(z)=a\) and \(Im(z)=b\)

Answer 6

Alright/ That makes a lot more sense. Also when you're looking for the absolute value, how do I do it when you have z = [1-isqrt(3)]*[sqrt(3) + 1] ?

Answer 7

that ,means I have to first simplify the expression THEN do the formula sqrt a^2 + b^2 ?

Answer 8

Yes.

Answer 9

Also, another way to find absolute value is to multiply by conjugate and take square root. \[
|z| = \sqrt{z\times \overline{z}}
\]

Answer 10

Alright. That helps even more.
If I have z_1 = -1/2 + i ; z_2 1 - 1/3i and - z_1 + z_2, z_1 - z_2 and z_1 * z_2
so I just replace z_1 and z_2 with the values?

Answer 11

Yes.

Answer 12

In the end \(i\) is treated like a variable. You only add up like terms.

Answer 13

How would I solve z - z complex conjugate / 1 + z * z complex conjugate (Im) if every z = x + iyand y =/= 0

Answer 14

x + iy
and *