Question

8. 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

Answer 1

a would be [(-3/sqrt{2})+i*(3/sqrt{2})\]

Answer 2

b would be -1+i*sqrt(3)

Answer 3

seems unlikely

Answer 4

first for a and second for b

Answer 5

sorry b willbe -1 -i*3/sqrt(2)

Answer 6

\[3(\cos(27°) + i\sin(27°))^5\] raise \(3^5\) to get \(343\) then multiply the angle by \(5\) to get
\[27\times 5=135\] so it is going to be
\[343\left(\cos(135)+i\sin(135)\right)\]

Answer 7

then evaluate the trig functions
\[\cos(135)=-\frac{\sqrt2}{2}, \sin(135)=\frac{\sqrt2}{2}\] and plug them in

Answer 8

3 is out of شقؤ

Answer 9

3 is out of arc so i still 3

Answer 10

\[343\left(\cos(135)+i\sin(135)\right)\]
\[=343\left(-\frac{\sqrt2}{2}+\frac{\sqrt2}{2}i\right)\]

Answer 11

So what Satellite said what the correct answer for a? Sorry I am a little bit confused

Answer 12

sqrt(2)/2 =1/sqrt(2)

Answer 13

the power is on the arc only but 3 is free so 3 still 3

Answer 14

i really doubt it

Answer 15

a will be [(-3/sqrt{2})+i*(3/sqrt{2})\]

Answer 16

b will be -1 -i*3/sqrt(2)

Answer 17

i think it is the right answer

Answer 18

I will try it :)