a+bic{\displaystyle {\frac {a+bi}{c}}} where a{\displaystyle a} and c{\displaystyle c} are real numbers and bi{\displaystyle bi} is an imaginary number.
ac+bci{\displaystyle {\frac {a}{c}}+{\frac {b}{c}}i} Then, simplify the fractions to their decimal form.
a+bic+di{\displaystyle {\frac {a+bi}{c+di}}} where a{\displaystyle a} and c{\displaystyle c} are real numbers, and bi{\displaystyle bi} and di{\displaystyle di} are imaginary numbers.
The conjugate has the form: c−di{\displaystyle {c-di}} Multiply by the conjugate: a+bic+di∗c−dic−di{\displaystyle {\frac {a+bi}{c+di}}*{\frac {c-di}{c-di}}}
ac+bd+bci−adic2+d2{\displaystyle {\frac {ac+bd+bci-adi}{c^{2}+d^{2}}}} Note that during the simplification process, multiplying two complex numbers means squaring i{\displaystyle i}, resulting in −1{\displaystyle -1}. Further simplify the complex numbers by adding the real and complex numbers and dividing each numerator term by the denominator.
