Question

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places.

Answer 1

Given:

`[8(cos30^o+isin30^o)][3(cos90^o+isin90^o)]`

Required:

We need to express the given form in rectangular form.

Step-by-step explanation:

`Use\text{ }cos30^o=0.8660,sin30^o=0.5,cos90^o=0,\text{ and }sin90^o=1.`

`=[8(0.8660+i0.5)][3(0+i(1))]`

`=[8*0.8660+i8*0.5)][i3*(1))]`

`=(6.928+i4)(i3)`

`=6.928(i3)+i4(i3)`

`=i20.784-12`

`=-12.0000+i20.7840`

`[8(cos30^o+isin30^o)][3(cos90^o+isin90^o)]=-12.0000+i20.7840`

Final answer:

We know that z =a+bi is called the rectangular form.

The rectangular expression of the given expression is

`-12.0000+20.7840i.`

The real part is -12.0000 and the imaginary part =20.7840.