1. ## Complex Number question.

z = i(2 - i)/(1 + 2i) - (2 - i)

For some unknown reason, I cannot get the right answer when expressing this in polar form. To start off, I multiply the fraction by:
(1 - 2i) / (1 - 2i)
The fraction then calculates to 5/-3. My second step is to move into the subtraction. This leaves me with the answer:
z = (11 - 3i) / -3
Therefore I would like to conclude that:
z = 11/-3 + i
Henceforth:
a = 11/-3
b = 1
Now I calculate range via:
r = sqrt(a^2 + b^2)
After that calculation there, I can already see that I've stuffed something up along the way. Would anyone care to enlighten me please?

C. Anderson

2. You wandered off immediately from the start.

(1+2i)(1-2i) = 5 -- How did you manage 3?

1^2 - (2i)^2 = 1 - 4i^2 = 1 - (-4) = 1 + 4 = 5

3. Originally Posted by Turkey
z = i(2 - i)/(1 + 2i) - (2 - i)

For some unknown reason, I cannot get the right answer when expressing this in polar form. To start off, I multiply the fraction by:
(1 - 2i) / (1 - 2i)
The fraction then calculates to 5/-3. My second step is to move into the subtraction. This leaves me with the answer:
z = (11 - 3i) / -3
Therefore I would like to conclude that:
z = 11/-3 + i
Henceforth:
a = 11/-3
b = 1
Now I calculate range via:
r = sqrt(a^2 + b^2)
After that calculation there, I can already see that I've stuffed something up along the way. Would anyone care to enlighten me please?