Question

Aye someone please help ?

Answer 1

The required rectangular form of the given complex polar form :

z1 = -3√2 - 3√2i

Explanation:

`z_1=6[\cos ((5\pi)/(4)) + i\sin((5\pi)/(4))]...........(1)\\\\Now,\cos ((5\pi)/(4))=\cos(\pi+(\pi)/(4))\\\\=-\cos((\pi)/(4))\\\\=-(1)/(√(2))\\\\And,\sin ((5\pi)/(4))=\sin(\pi+(\pi)/(4))\\\\=-\sin((\pi)/(4))\\\\=-(1)/(√(2))`

On substituting the obtained values in equation (1)

`z_1=6[(-1)/(√(2))-i\cdot (1)/(√(2))]\\\\\implies z_1=-3√(2)- 3√(2)\cdot i`

Hence, the required rectangular form of the given complex polar form :

z1 = -3√2 - 3√2i