How do you divide complex numbers?

Answer 1

When dividing complex numbers you must:

1. Write the problem in fractional form
2. Rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

You must remember that a complex number times its conjugate will give a real number.

a complex number 2+2i. the conjugate to this is 2-i1. Multiply both together gives a real number.

(2+2i)(2-2i) = 4 -4i + 4i + (-4i2) (and as i2 = -1) = 8

To divide a complex number by a real number simply divide the real parts by the divisor.

(8+4i)/2 = (4+2i)

To divide a real number by a complex number.

1. make a fraction of the expression 8/(2+2i)

2. multiply by 1. express 1 as a fraction of the divisor's conjunction. 8/(2+2i)*(2-2i)/(2-2i)

3. multiply numerator by numerator and denominator by denominator.

(16-16i)/8

4. and simplify 2-2i