When the divisor (that is, the denominator in the fraction) is a complex number with non-zero real and imaginary parts, you must rationalize the denominator using the complex conjugate. When you rationalize the denominator, you must also multiply the numerator by i. You may have forgotten the radical i in the denominator, or you may have made a mistake when you rationalized the denominator. Since i 2 = −1, the quotient is negative. When you rationalize the denominator, you have i 2 in the denominator. After simplifying the numerical parts of, you still have to rationalize the denominator because i is left in the denominator. Rationalize the denominator of by multiplying by. When you simplify the numerical parts of, you still have i in the denominator. Rearranging to put like terms together gives 5 – 3 + 3 i + i, and combining like terms gives the correct answer 2 + 4 i. Distributing the subtraction to the second complex number gives 5 + 3 i – 3 + i. You may have added instead of subtracting.

You probably forgot to distribute the subtraction to the imaginary part of the second complex number, leaving it as – i instead of + i. Instead, you should distribute the subtraction across the second complex number to get 5 + 3 i – 3 + i. You may have combined 5 + 3 from the first number (ignoring the i) and 3 – 1 from the second number (ignoring the i), giving that result of 8 - 2 = 6. Rearranging to put like terms together gives 5 – 3 + 3 i + i, and combining like terms gives 2 + 4 i.

Dividing complex numbers