Question

z=4+4i find exponential and polar form​

Answer 1

Step-by-step explanation:

4+4i=r(Cosθ+iSinθ)

⇒ rCosθ=4 and rSinθ=4.......(1)

⇒r²(Cos²θ+Sin²θ)=32 (squaring and adding 1)

⇒r²=32

⇒r=4√2

and Tanθ=1 (diving 1)

⇒θ=π/4

4+4i=4√2 [Cos(π/4)+iSin(π/4)] (which is polar form)

and 4+4i=4√2.e^(iπ/4) (which is exponential form)