Perform arithmetic operations on complex numbers (a + bi).
Complex Numbers
Z₁ = a + bi
Z₂ = c + di
Result
Z₁ + Z₂4.00 + 9.00i
Z₁ - Z₂2.00 - 5.00i
Z₁ × Z₂-11.00 + 23.00i
Z₁ / Z₂0.34 - 0.38i
Conj(Z₁)3.00 - 2.00i
Conj(Z₂)1.00 - 7.00i
About this calculator
Complex Arithmetic
A complex number is expressed as a + bi, where 'a' is the real part, 'b' is the imaginary part, and i is the square root of -1. We treat 'i' like a variable during addition and subtraction, but use i² = -1 during multiplication.
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Pro Tips
Multiplication: FOIL it, then replace i² with -1.
Division: Multiply numerator and denominator by the conjugate of the denominator.
Conjugate of a+bi is a-bi.
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Fun Facts
"Complex numbers were initially regarded as 'impossible' or 'fictitious' by early mathematicians."
"They are essential in electrical engineering (AC circuits) and quantum physics."
