Question

How is the product of a complex number and a real number represented on the complex plane?

Consider the product of −2+8i and 5.

Answer 1

The complex number −2+8i has modulus of (1. 2√17)

When −2+8i is multiplied by 5, the modulus of the product is (2. 10√17)

Multiplying a complex number by a real number results in a scalar of the complex number. The quadrant location of the complex number and its product with (3. a positive real number) are the same.

Answer 2

The product of the real and complex number given is -10+40i

Explanation:

The general form of a complex number is expressed as z = x+iy where

x is the real part and y is the imaginary part.

Given a complex and a real value as shown

z1 = −2+8i and z2 = 5+i0

Taking their product;

z1z2 = (−2+8i)(5+i0)

z1z2 = -10+0+40i+0

z1z2 = -10+40i

According to the product of the complex numbers, the resulting real part is -10 and the complex part is 40.

The representation on the complex plane is as shown in the attachment.