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.

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

Step-by-step 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.

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