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.

Explanation:

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

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

$=[8\times0.8660+i8\times0.5)][i3\times(1))]$

$=(6.928+i4)(i3)$

$=6.928(i3)+i4(i3)$

$=i20.784-12$

$=-12.0000+i20.7840$

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

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.