Answer
$13.5747+24.4894i$
Work Step by Step
First, we use the product theorem to multiply the absolute values and add the arguments:
$(4$ cis $19.25^{\circ})(7$ cis $41.75^{\circ})$
$=4(7)$ cis $(19.25^{\circ}+41.75^{\circ})$
$=28$ cis $(61.0^{\circ})$
Next, we change the expression into its equivalent form:
$=28$ cis $(61.0^{\circ})$
$=28 (\cos 61^{\circ}+i\sin 61^{\circ})$
Then, we use the calculator to solve the functions of $\cos$ and $\sin$ and simplify the expression:
$28 (\cos 61^{\circ}+i\sin 61^{\circ})$
=$28 [0.484807+i(0.874620)]$
=$13.5747+24.4894i$
