complex numbers

Question

If z₁ = 2 + 3i and z₂ = 1 - 2i, then z₁ × z₂ equals

RankGuru · Accepted Answer

1. **Distributive Property**: Multiply the two complex numbers like binomials:
   - $z_1 	imes z_2 = (2 + 3i)(1 - 2i)$
2. **Expansion**:
   - $= 2(1) + 2(-2i) + 3i(1) + 3i(-2i)$
   - $= 2 - 4i + 3i - 6i^2$
3. **Substitute $i^2 = -1$**:
   - $= 2 - i - 6(-1)$
   - $= 2 - i + 6$
4. **Combine Real and Imaginary**:
   - $= 8 - i$.

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