Write each expression in the standard form for a complex number, a + bi. a. [3(cos(27°)) + isin(27°)]^5 b. [2(cos(40°)) + isin(40°)]^6

[3(cos(27°)) + isin(27°)]^5

2.67 + 1.36i

[2(cos(40°)) + isin(40°)]^6

1.53 + 1.29i  

step-by-step explan mxfcg'k; uafwgzfgjhklhgation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb