I need to know how.... (complex numbers)?

Question

I've been solving a math problem about complex number then suddenly I stopped at [1.116 (cos 306.54 + isin 306.54)] [4+4i]

I don't know how to continue on whether changing
[1.116 (cos 306.54 + isin 306.54)] in rectangular form then perform the operation or would it be [4+4i] to be transformed to its polar/trigonometric form then multiply the terms the usual way on how we multiply complex number in its trigonometric form. I also needed the logic behind it. Thanks!

Answer 1

Multiplying in polar is so much easier the foiling because you don't have to worry about the powers of i and its a lot less work.

turn 4+4i into polar coordinate r, theta
r=sqrt(a^2+b^2)
Theta = Arctan b/a
r= sqrt 32 == 4*sqrt 2
theta = arctan 4/4 =arctan 1 = 45 ,225,..
Graphing 4+4i in rectangular form puts it in the first quadrent
so you would use 45 degrees
you would then get
[(4*sqrt2) *(cos 45 + isin 45)]

Multiplying them gets [6.31305 *(cos 351.54 + isin 351.54)
Simplify
[6.31305 *(.98912 + i*(-.14712)]
and your answer is
[6.24436 -.92877i]

Answer 2

You can definately just multiply out [1.116 (cos 306.54 + isin 306.54)] *[4+4i] in the normal distributive way (FOIL, right?) just like you would something like
(x+3y)(2x+y). Just remember that i^2 = -1 and if you multiply out correctly, you'll have your answer. Converting to polar form and doing it is possible too, but it's a lot more work.

Answer 3

It would be easier to convert 4+4i to trig form and multiply.
To understand trig form, plot 4+4i. Draw a right triangle by connecting the origin to 4+4i, dropping a perpendicular to the real axis, and connecting the origin to the point on the real axis. The length of the hypotenuse is 2sqrt(2). The segment along the real axis is 2sqrt(2)cos45=4 and the vertical segment is 2sqrt(2)sin45=4.
4+4i=2sqrt(2)cos45+i2sqrt(2)cos45=
2sqrt(2)[cos45+isin45] which is trig form.

Answer 4

= 1.116 [ 0.595 - i 0.803] [ 4 + 4i ]
= 1.116 [ 2.38 + 2.38i - 3.21 i + 3.31]
= 1.116 [ 5.69 - 0.83 i ]
= 6.35 - 1.03 i

Answer 5

euler???