Find the absolute values of z if 2z-i +5 = 3z -3i +1

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We have to find the absolute value of z given that 2z-i +5 = 3z -3i +1

2z - i + 5 = 3z -3i +1

=> 3z - 2z = -i + 3i + 5 -1

=> z = 2i + 4

The absolute value of z is given by sqrt ( 2^2 + 4^2)

=> sqrt ( 4 + 16)

=> sqrt 20

Therefore the absolute value of z is sqrt 20.

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Given the complex equation:

2z -i + 5 = 3z -3i +1

We need to find the absolute value of z.

First we need to rewrite z into the format of the complex number z = a+bi

let us combine terms with z on the left side.

==> 2z -3z = -3i +1 +i -5

==> -z = -4 -2i

Now we will multiply by -1

==> z = 4 + 2i

Now we will calculate the absolute values.

==> l z l = sqrt(a^2 + b^2)

               = sqrt( 4^2 + 2^2)

               = sqrt(16 + 4) = sqrt20 = 2sqrt5

==> l zl = 2sqrt5

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