3i45i answer as complex numbers in standard form 3i divided

-3i/-4-5i answer as complex numbers in standard form

-3i divided by -4-5i

-3i/(-4-5i)

=-3i/(-(4+5i))

=3i/(4+5i)

multiply and divide numerator and denominator by conjugate of denominator 4-5i

=(3i(4-5i))/((4+5i)(4-5i))

=((3i*4)-(3i*5i))/(4²-(5i)²)

=((12i)-(-15))/(16-(-25))

=(12i+15)/(16+25)

=(12i+15)/(41)

=(12/41)i+(15/41)

=(15/41)+(12/41)i

-3i/(-4-5i) =(15/41)+(12/41)i