multiplying complex numbers

Question

Multiply 

 

(3-i)(6-6i) 

 

write answer as a complex number in standard form 

Answer 1

Complex numbers in standard format following the convention of ...

z = x + iy

Define z₁ = (3 - i)

Define z₂ = (6 - 6i)

z₁* z₂ follows the factorization methods we use for multinomial (polynomial) representations...

z₁ * z₂ = 3 * 6 + 3 * (-6i) + 6 * (-i) + (-i) * (-6i)

z₁ * z₂ = 18 - 18i -6i + 6i2

z₁ * z₂ = 18 - 24i + 6(-1)

z₁ * z₂ = 12 -24i = 12(1 - 2i)