7。 Given the complex number w-4=(3-2w)i, z=(5/w)+∣w-2∣, find a real coefficient quadratic equation with z as the root.

Solution: w-4=(3-2w)i, (1+2i)w=4+3i, so w = (4+3i)/( 1+2i) = (4+3i)/.

So z = [5/(2-I)]+∣ 2-I-2 ∣ = 5 (2+I)/5+∣-I ∣ = 2+I+1= 3+I.

If a quadratic equation with one variable has a complex root, then there must be another complex root conjugated with this complex root, that is, if there is a complex root 3+i, then it must be.

There is also a 3-I.

To simplify the calculation, take a= 1, x? =3-i，x？ =3+i，x？ +x？ =(3-i)+(3+i)=6，x？ x？ =(3-I)(3+I)= 9+ 1 = 10；

So the unary quadratic equation is x? -6x+ 10=0

8。 Univariate quadratic equation ax? +bx+c=0 has two imaginary roots x? ，x？ ; And (1-3ai)i=c-(a/i), ∣x? -x？ ∣= 1. The value of the real number b.

Solution: From (1-3ai)i=c-(a/i) to -( 1-3ai)=ci-a, so there is (3a-c)i= 1-a, ∴ a = 65438.

∣x？ -x？ ∣=√(x？ -x？ )? =√[(x？ +x？ )? -4x？ x？ ]=√[(-b)？ -4c]=√[(-b)？ -12]= 1, that is to say ∣b? -12∣= 1, absolute value sign

B in the movie? - 12=b？ -4ac=△, because it is an imaginary root, △ < 0, so we should take b? -12=- 1, that is, b? = 1 1; That is b = √ 1 1.