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(1-9i)(3+2i)=0
We add all the numbers together, and all the variables
(-9i+1)(2i+3)=0
We multiply parentheses ..
(-18i^2-27i+2i+3)=0
We get rid of parentheses
-18i^2-27i+2i+3=0
We add all the numbers together, and all the variables
-18i^2-25i+3=0
a = -18; b = -25; c = +3;
Δ = b2-4ac
Δ = -252-4·(-18)·3
Δ = 841
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{841}=29$$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-29}{2*-18}=\frac{-4}{-36} =1/9 $$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+29}{2*-18}=\frac{54}{-36} =-1+1/2 $
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