What is the value of the expression given below? (5+3i) - (5+3i)(5-5i

Solution:

The given complex expression is,

→(5+3 i) - (5+3 i)(5-5 i)

Keep in mind, i=√-1, i²= -1

=(5 + 3 i)[1- (5-5 i)]

=(5 + 3 i)[1-5+ 5 i]

= (5 + 3 i)[-4 + 5 i]

=5 × (-4 + 5 i) + 3 i×(-4 + 5 i)→→Used the identity, (a+b)×(c+d)=a×(c+d)+b×(c+d), Also Used distributive property of multiplication over addition and subtraction.

= -20 + 25 i-12 i +15 i²

= - 20 + 13 i-15

= -35 + 13 i

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)