Question

How do you simplify `(-5-3i)/(4i)` and write the complex number in standard form?

Answer 1

`-3/4+5/4i`

Explanation:

To simplify, we require to multiply the numerator and denominator by the `color(blue)"complex conjugate"` of the denominator.

Given a complex number z = x ± yi then the complex conjugate is.

`color(red)(|bar(ul(color(white)(a/a)color(black)(barz=x∓yi)color(white)(a/a)|)))`

Note that the real part remains unchanged while the `color(blue)"sign"` of the imaginary part is reversed.

Example: z = 5 + 4i then complex conjugate is `barz=5-4i`

Here z = 4i = 0 + 4i in standard form.Thus the complex conjugate is - 4i

Multiply numerator and denominator by - 4i

`rArr((-5-3i)color(red)"-4i")/(4ixxcolor(red)"-4i")=(20i+12i^2)/(-16i^2)`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(i^2=(sqrt(-1))^2=-1)color(white)(a/a)|)))`

`rArr(20i+12i^2)/(-16i^2)=(20i-12)/16=(-12)/16+20/16i`

`rArr(-5-3i)/(4i)=-3/4+5/4i" in standard form"`