Question

I si

what is w- z expressed in polar form?
Given wuv5c() + (.) and : ==(--(?) + ()
=(cos1 - +(cosin
o vz(cos() + i sin (4)
o v7(com () + ()
ovi (95) + ()
o r2(com () + i sin (7)
COS
i sin
ST
COS
+ i sin
77
o
+

Answer 1

`w-z=√(2)\biggr(cos((3\pi)/(4))+isin((3\pi)/(4))\biggr)`

Explanation:

Convert from polar to rectangular

`w=√(2)(cos((\pi)/(4))+isin((\pi)/(4)))\\\\w=√(2)((√(2))/(2)+(√(2))/(2)i)\\ \\w=1+i`

`z=2(cos((\pi)/(2))+isin((\pi)/(2)))\\ \\z=2(0+i)\\\\z=2i`

Subtract the complex numbers

`w-z=(1+i)-2i=1+i-2i=1-i`

Convert from rectangular (x,y) to polar (r,θ)

`r=√(x^2+y^2)\\r=√(1^2+(-1)^2)\\r=√(1+1)\\r=√(2)\\\\\theta=tan^(-1)((y)/(x))\\ \theta=tan^(-1)((-1)/(1))\\ \theta=tan^(-1)(-1)\\\theta=(3\pi)/(4)\\ \\w-z=√(2)\biggr(cos((3\pi)/(4))+isin((3\pi)/(4))\biggr)`