What is the answer to im(1/(x+yi))= 1/2 ?

The answer to im(1/(x+yi))= 1/2 is x=0,y=2m

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im(1/(x+yi))= 1/2

im (\frac{1}{x + y i}) = \frac{1}{2}

x = 0, y = 2 m

Solution steps

im (\frac{1}{x + y i}) = \frac{1}{2}

Multiply both sides by

2

im \frac{1}{x + y i} \cdot 2 = \frac{1}{2} \cdot 2

Simplify

\frac{2 im}{x + i y} = 1

Multiply both sides by

x + i y

\frac{2 im}{x + i y} (x + i y) = 1 \cdot (x + i y)

Simplify

2 im = x + i y

Rewrite

2 im

in standard complex form:

0 + 2 mi

0 + 2 mi = x + i y

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

[0 = x 2 m = y]

[0 = x 2 m = y] : x = 0, y = 2 m

x = 0, y = 2 m

z^{2} = - \frac{4}{3} i

5 x^{2} + b = (5 x + 8 i) (5 x - 8 i)

x + (x - y) i = 4 i

a^{2} + b^{2} + 1 + 12 i = 6 (a + bi)

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

What is the answer to im(1/(x+yi))= 1/2 ?
The answer to im(1/(x+yi))= 1/2 is x=0,y=2m