What is the answer to ((41+3i))/(65)= 1/x ?

The answer to ((41+3i))/(65)= 1/x is x= 41/26-3/26 i

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((41+3i))/(65)= 1/x

\frac{( 41 + 3 i )}{65} = \frac{1}{x}

x = \frac{41}{26} - \frac{3}{26} i

Solution steps

\frac{( 41 + 3 i )}{65} = \frac{1}{x}

Substitute

x = a + bi

\frac{41 + 3 i}{65} = \frac{1}{a + bi}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(41 + 3 i) (a + bi) = 65 \cdot 1

Expand

(41 a - 3 b) + i (3 a + 41 b) = 65

Rewrite

65

in standard complex form:

65 + 0 i

(41 a - 3 b) + i (3 a + 41 b) = 65 + 0 i

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

[41 a - 3 b = 65 3 a + 41 b = 0]

[41 a - 3 b = 65 3 a + 41 b = 0] : a = \frac{41}{26}, b = - \frac{3}{26}

Substitute back

x = a + bi

x = \frac{41}{26} - \frac{3}{26} i

i x^{2} - 2 (i + 1) x + 10 = 0

s i y = 33 y + 1

\frac{1 + 4 i}{3 - 6 i} = a + bi

z^{2} + (1 - 2 i) z + 1 + 5 i = 0

a^{2} + 2 abi - b^{2} = 2 i

What is the answer to ((41+3i))/(65)= 1/x ?
The answer to ((41+3i))/(65)= 1/x is x= 41/26-3/26 i