If |z1| = 3 and |z2| = 4, what is |z1 z2|?

If |z1| = 3 and |z2| = 4, what is |z1 z2|?

• A. 7
• B. 12
• C. 1
• D. 0

Answer: (B)

The key idea is that the modulus (distance from the origin) of a product of complex numbers multiplies: |z1 z2| = |z1| · |z2|. With |z1| = 3 and |z2| = 4, the magnitude of the product is 3 × 4 = 12. So the answer is 12. The other options don’t follow from the multiplicative property of moduli: you don’t add magnitudes or get zero unless one factor is zero, and 1 would require a magnitude of 1 for the second factor.

The key idea is that the modulus (distance from the origin) of a product of complex numbers multiplies: |z1 z2| = |z1| · |z2|. With |z1| = 3 and |z2| = 4, the magnitude of the product is 3 × 4 = 12.

So the answer is 12. The other options don’t follow from the multiplicative property of moduli: you don’t add magnitudes or get zero unless one factor is zero, and 1 would require a magnitude of 1 for the second factor.