nice-calculus-suppose-z-x-iy-amp-z-1-3-p-iq-then-find-A-x-p-y-q-p-2-q-2-note-i-1-

Question Number 125096 by mnjuly1970 last updated on 08/Dec/20

\dots n i c e c a l c u l u s \dots

s u p p o s e :: z = x - i y & \sqrt[3]{z} = p + i q

t h e n f i n d :: A = \frac{\frac{x}{p} + \frac{y}{q}}{p^{2} + q^{2}} = ? ?

n o t e : i = \sqrt{- 1}

Answered by MJS_new last updated on 08/Dec/20

\sqrt[3]{z} = p + q i \Rightarrow z = p (p^{2} - 3 q^{2}) - q (q^{2} - 3 p^{2}) \Rightarrow

\Rightarrow x = p (p^{2} - 3 q^{2}) \land y = q (q^{2} - 3 p^{2})

\Rightarrow A = - 2

Commented by mnjuly1970 last updated on 08/Dec/20

t h a n k s a l o t s i r M J S . g r a t e f u l . .