Help Checking a Complex Numbers Problems

[jisbon]

Homework Statement

Various Complex Number Questions

Relevant Equations

NIL

Hello, here with some complex number questions which I need some assistance in checking :)

1)
z=3+5i1+3iz=3+5i1+3i
Find Re(z) and Im(z)
My answer is 9595 and −25−25 respectively.
Checked by Wolfram
2)
Find principal argument of the complex numberz=−5+3iz=−5+3i and express it in radians up to 2 decimal places
My answer is 2.60
Checked by Wolfram
3)
z=sin(8t)+i(1−cos(8t))z=sin(8t)+i(1−cos(8t))
Find arg(z) and mod(z) in terms in t
Since mod(z) is just the root of a square + b square, the answer is as follows.
As for arg(z),

My answer is 4t and √((sin(8t))2+((1−cos(8t)2)((sin(8t))2+((1−cos(8t)2)

4)
Let z be complex number with Re(z) = 1/2 and mod z = 1
Evaluate (1+iz)(1+¯¯¯z2)1−i¯¯¯z(1+iz)(1+z¯2)1−iz¯

My answer is 1i

5)
Find value of z such as mod z - z =3+ 9i

My answer is 12-9i

6)
Find z that satisfies z2+7¯¯¯z=0

z2+7z¯=0
My answer is 72+7√32i72+732i

7)
Suppose z is a non-zero complex number satisfying (8+i)z=(8−i)¯¯¯z(8+i)z=(8−i)z¯ Find ratio of Im(z)/Re(z)

My answer is -1/8

8)
If z = a+ib, and is a solution to z2−z+4=0z2−z+4=0 , find a and b
My answer is 0.5 and √152152
Checked by Wolfram

 

[mfb]

Please include the intermediate steps.
WolframAlpha can do a lot of these checks directly.

 

[Delta2]

1 and 2 seem correct to me.
for 3 I have my doubts about arg(z)
for 4 I found the expression to be simpy i.
5 seems correct to me.

 

[jisbon]

1 and 2 seem correct to me.
for 3 I have my doubts about arg(z)
for 4 I found the expression to be simpy i.
5 seems correct to me.

Updated 4 and 3 with workings :)

 

[Delta2]

Glad we agreed for 4. Easiest way to do it if you know the relations that $z+\bar{z}=2Re(z)$ and $z\bar{z}=|z|^2$ without the need to calculate the imaginary part of z.

For 3 seems you were correct afterall, I completely forgot that trigonometric identity .
7 seems also correct to me.

You should repost the statement and work on 6 cause something is wrong there...

 

[jisbon]

Glad we agreed for 4. Easiest way to do it if you know the relations that $z+\bar{z}=2Re(z)$ and $z\bar{z}=|z|^2$ without the need to calculate the imaginary part of z.

For 3 seems you were correct afterall, I completely forgot that trigonometric identity .
7 seems also correct to me.

You should repost the statement and work on 6 cause something is wrong there...

uploaded :)

 

[FactChecker]

I find your typed formulas to be incomprehensible. There are many unbalanced parentheses, run-on formulas that I can't tell if they are new equations, etc. If you want serious help, then you should make a better effort to make your questions readable.

 

[jisbon]

I find your typed formulas to be incomprehensible. There are many unbalanced parentheses, run-on formulas that I can't tell if they are new equations, etc. If you want serious help, then you should make a better effort to make your questions readable.

Yep I understand. For some reason, whenever I try to edit some of the stuff below, the equations in the area above seems to glitch out and repeats itself :/ Not sure what is happening.