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Math Formulas > Complex Number > Operations

Operations

Addition - complex number
(a + bi) + (c + di) = (a + c) + (b + d)i

Example:
z1 = 3 - 4i and z2 = -2 + 2i
z1 + z2 = (3 + (-2)) + (-4 + 2)i = 1 -2i

Subtraction - complex number
(a + bi) - (c + di) = (a - c) - (b - d)i

Example:
z1 = 3 - 4i and z2 = -2 + 2i
z1 - z2 = (3 - (-2)) - (-4 - 2)i = 5 +6i

Multiplication - complex number
(a + bi) ∙ (c + di) = (ac - bd) + (bc + ad)i = ac + bci + adi + bdi2

Example:
z1 = 3 - 4i and z2 = -2 + 2i
z1 ∙ z2 = (3 ∙ (-2)) + (-4 ∙ (-2))i + (3 ∙ 2)i + (-4 ∙ 2)i2 = -6 + 14i -8i2

Division - complex number
(a + bi)/(c+di) = (ac + bd)/(c2 + d2) + (bc - ad)/(c2 + d2)i

Example:
z1 = 3 - 4i and z2 = -2 + 2i
z1 / z2 = (3 ∙ (-2) + (-4 ∙ 2))/((-2)2 + 22) + (-4 ∙ (-2) - 3 ∙ 2)/((-2)2 + 22)i = -14/8 + (2/8)i = -7/4 + i/4


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