Question

Write the complex number in the form a + bi.

square root of six(cos 315° + i sin 315°)

Answer 1

I dont know how to solve this at all...
My choices:
square root of three over two minus square root of thee over two times i
square root of six minus square root of sixi
square root of three minus square root of threei
square root of six over two minus square root of six over two times i

Answer 2

look at the unit circle
cos 315 = what ?
remember (x,y) sin =y-coordinate and
cos = x-coordinate

Answer 3

cos315 is square root(2)/2

Answer 4

so \[\frac{ \sqrt{2} }{ 2 }\] is my x coordinate?

Answer 5

Yes, I was just looking at that

Answer 6

\[\huge\rm \sqrt{6}(\cos 315° + i \sin 315°)\]
so cos 315 =sqrt{2} over 2
replace cos 315 by that

Answer 7

So i would replace isin315 with \[\frac{ -\sqrt{2} }{ 2 }\]

Answer 8

@Nnesha Good job!! open my eye!! :)

Answer 9

\[\huge\rm \sqrt{6}(\color{reD}{cos 315°} + i \sin 315°)\]
\[\sqrt{6}(\frac{ \sqrt{2} }{ 2 }+i (-\frac{ \sqrt{2} }{ 2 }))\]
ust sin315 not the i

Answer 10

just**

Answer 11

Alright, then do I distribute the \[\sqrt{6}\]?

Answer 12

thanks o^_^o @66

Answer 13

first distribute by i
i times -sqrt{2} over 2

Answer 14

\[\sqrt{6}(\frac{ \sqrt{2} }{ 2} - \frac{ \sqrt{2} }{ 2}i)\]

Answer 15

Okay, after distributing i, do I distribute the square root of 6?

Answer 16

well i wouldn't do that
just take out the common factor

Answer 17

\[\sqrt{6}\color{ReD}{(\frac{ \sqrt{2} }{ 2} - \frac{ \sqrt{2} }{ 2}i)}\]

what is common factor in the parentheses

Answer 18

Hmm... then my end result is \[\sqrt{3}(-i+1)\]

Answer 19

u sure or just guessing ? ;P

Answer 20

100% sure. I just calculated it. If I distribute the square root of 3, then I get what appears to be my third choice. Am I correct?

Answer 21

alright yes that's correct
there are square roots that's why i don't like distributing by sqrt{6} you can take out the common factor which is sqrt{2}/2

Answer 22

Oh, I see. @Nnesha

Answer 23

\[\sqrt{6} \times \frac{ \sqrt{2} }{ 2 }(1-i)\]
\[\frac{ \sqrt{12} }{ 2 }(1-i)\]multply sqrt{6} times sqrt{2}
now factor 12
\[\frac{ \sqrt{4 \times 3} }{ 2}(1-i)\]
take the square root of 2
you will get the same answer

Answer 24

i found it easy but you can apply any method as lng s you get the same answer