calculate the absolute value of z if z = 2z' -3+5i

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the given equation z = 2z' - 3 + 5i

Let z = a + ib

z = 2z' - 3 + 5i

=> a + ib = 2a - 2b*i - 3 + 5i

=> a + ib = 2a - 3 - 2b*i + 5i

equate the real and complex coefficients

=> a = 2a - 3 and b = 5 - 2b

=> a = 3 and 3b = 5

z = 3 + (5/3)i

The absolute value is sqrt (3^2 + (5/3)^2)

=> sqrt (9 + 25/9)

=> sqrt ( 106/9)

=> (sqrt 106)/3

The absolute value of z is (sqrt 106)/3

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let z= a+ bi

==> z' = a- bi

We will substitute.

==> a+ bi = 2a-2bi -3 + 5i

==> -a + 3bi = -3 + 5i

==> a= 3

==> b= 5/3

==> z = 3+ (5/3)i

==> l zl = sqrt(3^2+(5/3)^2

             = sqrt(9+ 25/9) = sqrt(106/9) = sqrt(106) / 3

Then the absolute value of z is l z l = sqrt(106) / 3

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