I have the following problem:
Solve the quadratic equation: (1-i)*z^2+(1+3i)z+(-4+2i)=0
So what I tried is: a=1-i, b=1+3i, c=-4+2i
Then plugged them inside the quadric formula, and eventually got:
z1,2 = -(1+3i)+-sqrt( (1+3i)^2 -4 (1-i)(-4+2i) ) / 2(1-i)
...
= (-1-3i+-sqrt(-18i)) / 2-2i
now I guess this sqrt(-18i) should be broken up somehow...so:
1) sqrt(-18i)=sqrt(18)*sqrt(-i)
sqrt(18) = sqrt(9*2)=3*sqrt(2)
2) sqrt(-i) = sqrt( - sqrt(-1) ) = ...?
what can I break this down...? or can't I?
Thanks.
Solve the quadratic equation: (1-i)*z^2+(1+3i)z+(-4+2i)=0
So what I tried is: a=1-i, b=1+3i, c=-4+2i
Then plugged them inside the quadric formula, and eventually got:
z1,2 = -(1+3i)+-sqrt( (1+3i)^2 -4 (1-i)(-4+2i) ) / 2(1-i)
...
= (-1-3i+-sqrt(-18i)) / 2-2i
now I guess this sqrt(-18i) should be broken up somehow...so:
1) sqrt(-18i)=sqrt(18)*sqrt(-i)
sqrt(18) = sqrt(9*2)=3*sqrt(2)
2) sqrt(-i) = sqrt( - sqrt(-1) ) = ...?
what can I break this down...? or can't I?
Thanks.