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##