What is -4-3i divided by 4 plus i?

Answer 1

To divide by a complex number, write it as a fraction and then multiply the numerator and denominator by the complex conjugate of the denominator - this is formed by changing the sign of the imaginary bit of the number; when a complex number (a + bi) is multiplied by its complex conjugate the result is the real number a² + b² which can be divided into the complex number of the numerator:

(-4 - 3i) ÷ (4 + i)

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

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

= (-16 + 4i - 12i + 3i²) / (4² + 1²)

= (-16 - 8i - 3) / (16 + 1)

= (-19 - 8i)/17

Answer 2

The way you solve this is to multiply top and bottom by the complex conjugate of the denominator (bottom). In this case, the complex conjugate of 4+i is 4-i (just flip the sign of the imaginary part to get the complex conjugate), so you multiply top and bottom by 4-i, and do the calculations. This will let you cleanly separate the real and the imaginary part.When doing the calculations, remember that i squared = -1.

Answer 3

It is (-19 - 11i)/17