2/3i-i=-1/3i

Solution for 2/3i-i=-1/3i equation:

2/3i-i=-1/3i

We move all terms to the left:

2/3i-i-(-1/3i)=0


Domain of the equation: 3i!=0

i!=0/3

i!=0

i∈R



Domain of the equation: 3i)!=0

i!=0/1

i!=0

i∈R


We add all the numbers together, and all the variables

-1i+2/3i-(-1/3i)=0

We get rid of parentheses

-1i+2/3i+1/3i=0

We multiply all the terms by the denominator


-1i*3i+2+1=0

We add all the numbers together, and all the variables

-1i*3i+3=0

Wy multiply elements

-3i^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$