How do you find the multiplicative inverse of 5+2i in standard form?

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Answer 1 · 2016-01-13T05:23:25

The explanation is given below.

The multiplicative inverse of $z$ is $1/z$ where $z(1/z) = 1$

In our problem, we have $z=5+2i$ we need to find $1/z$

Which would be, $1/(5+2i)$

$1/(5+2i) = 1/(5+2i)*(5-2i)/(5-2i)$

Multiply numerator and denominator by the conjugate of the denominator and make the denominator a real number.

$1/(5+2i) = (5-2i)/(5^2-(2i)^2)$

$1/(5+2i) = (5-2i)/(25+4)$

$1/(5+2i) = (5-2i)/29$

$1/(5+2i) = 5/29 - 2/29i$

The multiplicative inverse is $5/29 - 2/29i$ #