Perform the indicated operation
(1 – 3i)(5 + 5i)(4 – 1i) =

70-60i

Step-by-step explanation:

(1 – 3i)(5 + 5i)(4 – 1i) =

taking the first two, before we do the last one

(1 – 3i)(5 + 5i)

1(5+5i)-3i(5+5i)

1(5)+1(5i)-3i(5)-3i(5i)

5+5i-15i-15i²

from the miltiplication law, i² is -1

5-10i-15i² = 5-10i-15(-1) = 5-10i+15 = 5+15-10i = 20-10i

then multiply (20-10i) (4 – 1i)

20(4 – 1i)-10i(4 – 1i)

20(4)-20(1i)-10i(4)-10i(-1i)

80-20i-40i+10i²

80-60i+10(-1)

80-60i-10

80-10-60i

(1 – 3i)(5 + 5i)(4 – 1i) =70-60i

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225