Question

What is the standard form of (2+3i)(4-7i)/(1-I)

Answer 1

I believe in standard form this would be 31/2 + 27i/2

Answer 2

Standard form is a+bi where a is the real part and bi is the imaginary part

we need to rationalize the denomenator

remember difference of 2 perfect squares
(a-b)(a+b)=a²-b²
so

in denom we got (1-i)
mulitply whole fraction by (1+i)/(1+i)
(2+3i)(4-7i)(1+i)/(1²-i²)
(2+3i)(4-7i)(1+i)/(1-(-1))
(2+3i)(4-7i)(1+i)/(1+1)
(2+3i)(4-7i)(1+i)/(2)
simplfy top part
(31+27i)/2
31/2+27i/2


the standard form is
$\frac{31}{2}+ \frac{27}{2}i$