What is the complex number z from identity 3z18z12iSolutionW

What is the complex number z from identity 3z-18z\'=12+i?

Solution

We\'ll consider z\' as being the conjugate of z, therefore z = a + bi and z\' = a - bi.

We\'ll replace z and z\' by its rectangular forms, into the given identity:

3(a+bi) - 18(a - bi) = 12 + i

We\'ll remove the brackets:

3a + 3bi - 18a + 18bi = 12 + i

We\'ll combine real parts and imaginary parts form the left side:

-15a + 21bi = 12 + i

Comparing, we\'ll get:

-15a = 12 => a = 12/-15 => a = -4/5

21b = 1 => b = 1/21

The requesed complex number is: z = -4/5 + i/21.