We'll write the rectangular form of the complex number
z:
z = a + bi
Since z' is the
conjugate of z, then z' = a - b.
To determine z, we'll
have to find out it's coefficients:
We'll multiply by 6
both sides:
3(a + bi) - 2(a - bi) = -
30
We'll remove the
brackets:
3a + 3bi - 2a + 2bi = -
30
We'll move all terms to the left
side:
3a + 3bi - 2a + 2bi + 30 =
0
We'll combine real parts and imaginary
parts:
a + 5bi + 30 = 0
The
real part of the complex number from the left side
is:
Re(z) = a + 30
The real
part of the complex number from the right side is:
Re(z) =
0
Comparing, we'll get:
a + 30
= 0
a = -30
The imaginary part
of the complex number from the left side is:
Im(z) =
5b
The imaginary part of the complex number from the right
side is:
Im(z) = 5b
Comparing,
we'll get:
5b = 0
b =
0
The requested complex number z is:
z = -30 (whose imaginary part is
0).
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