Question

graph the complex number as a vector in the complex plane. 4 + 7i choose the correct graph of the vector.

Explanation:

Step1: Recall complex number plotting

A complex number \(a + bi\) is plotted with real part \(a\) on the x - axis and imaginary part \(b\) on the y - axis. For \(4 + 7i\), real part \(a = 4\) (positive, so right on x - axis) and imaginary part \(b=7\) (positive, so up on y - axis).

Step2: Analyze each option

• Option A: The vector has real part positive (around 4) and imaginary part positive (around 7), matching \(4 + 7i\).
• Option B: Real part seems negative, doesn't match \(a = 4\).
• Option C: Real part negative, imaginary part negative, doesn't match.
• Option D: Real part positive but imaginary part negative, doesn't match \(b = 7\).

Answer:

A. (The graph corresponding to Option A, which has a vector with real part 4 (right on x - axis) and imaginary part 7 (up on y - axis))