If z1 = a + bi and z2 = c + di, and z1 = z2, which must be true?

If z1 = a + bi and z2 = c + di, and z1 = z2, which must be true?

• A. a = c and b = d
• B. a = d and b = c
• C. a = c or b = d
• D. a ≠ c or b ≠ d

Answer: (A)

The real and imaginary parts must match when two complex numbers are equal. If a + bi equals c + di, then comparing real parts gives a = c and comparing imaginary parts gives b = d. Therefore, both conditions must hold. If either part differed, the two numbers would not be the same.

The real and imaginary parts must match when two complex numbers are equal. If a + bi equals c + di, then comparing real parts gives a = c and comparing imaginary parts gives b = d. Therefore, both conditions must hold. If either part differed, the two numbers would not be the same.