CSCAPrep
Reviewed CSCA Mathematics question · Hard

Let z = 4 - 3i and w = -2 + i. What is the real part of z * w?

  1. -11
  2. -5
  3. 5
  4. 11
Show the answer and explanation

Correct answer

B. -5

Principle or equation

To multiply complex numbers, use the distributive property and i^2 = -1. For (a+bi)(c+di), the real part is ac - bd.

Why this answer is correct

Compute (4 - 3i)(-2 + i) = -8 + 4i + 6i - 3i^2 = -8 + 10i + 3 = -5 + 10i. The real part is -5.

Example

For (2+3i)(1-i), real part = 2*1 - 3*(-1) = 5.

This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.

Related practice questions

Easy · Geometry and algebraWhat is the product (2 + 3i)(1 - i)?Standard · Geometry and algebraWhat is the center of the circle given by x^2 + y^2 - 4x + 6y - 3 = 0?Easy · Geometry and algebraGiven vectors u = (3, -2) and v = (1, 4), what is 2u - v?Easy · Geometry and algebraA rectangular box has vertices at (0,0,0), (4,0,0), (0,3,0), and (0,0,12). What is the length of the space diagonal of this box?Standard · Geometry and algebraWhat is the value of (3 + 2i) / (1 - i)?