What is the answer to i=(\sqrt[3]{6})/((r-2)) ?

The answer to i=(\sqrt[3]{6})/((r-2)) is r=2-\sqrt[3]{6}i

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i=(\sqrt[3]{6})/((r-2))

Solution steps

Substitute

r = x + y i

Multiply both sides by

x - 2 + i y

Simplify

Rewrite

in standard complex form:

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

Substitute back

r = x + y i

x + y i - \frac{1}{x + y i} = 1 + 4 i

4 z^{2} + (4 - 4 i) z + 5 - 2 i = 0

- 1 + 2 i = \frac{2 i}{( z - 1 )}

- x + y i + 7 = 6 i

0 = z^{2} + i z - 6

What is the answer to i=(\sqrt[3]{6})/((r-2)) ?
The answer to i=(\sqrt[3]{6})/((r-2)) is r=2-\sqrt[3]{6}i