complex number multiplication by a real number

Question

I'd like to multiply a complex value by a real integer. I know that multiplication of complex numbers is similar in the polar form, but the way I know and have been taught is to multiply the two real components then add the angles. What do I do when I have no angle and just a real number as the multiplier :

0.08∠76° ∙100

Best regards Danny J

Answer 1

Let's say you have $0.08 \ \text{cis}\ 76^{\circ}$ and you want to multiply it by $100$. Just multiply the real number out from by $100$, so your answer is:

$$0.08 \ \text{cis}\ 76^{\circ} \cdot 100=8 \ \text{cis}\ 76^{\circ}$$