Mathematics is the queen of the sciences.C. F. Gauss

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Complex numbers

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6

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Addition

Formulas

ℜ(z)=ar+br\Re(z)=a_r+b_rℑ(z)=ai+bi\Im(z)=a_i+b_iℜ(z)=ar−br\Re(z)=a_r-b_rℑ(z)=ai−bi\Im(z)=a_i-b_iℜ(z)=arbr−aibi\Re(z)=a_rb_r-a_ib_iℑ(z)=arbi+aibr\Im(z)=a_rb_i+a_ib_rℜ(z)=arbr+aibibr2+bi2\Re(z)=\frac{a_rb_r+a_ib_i}{b_r^2+b_i^2}ℑ(z)=aibr−arbibr2+bi2\Im(z)=\frac{a_ib_r-a_rb_i}{b_r^2+b_i^2}∣z∣=x2+y2|z|=\sqrt{x^2+y^2}φ=atan2⁡(y,x)\varphi=\operatorname{atan2}(y,x)

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