How do you simplify #(1-isqrt2)/(1+isqrt2)#?

1 Answer
Apr 16, 2018

Answer:

#=-1/3(1+2sqrt2i)#

Explanation:

Expression #=(1-isqrt2)/(1+isqrt2)#

Rationalise the denominator by multiplying the expression by #(1-isqrt2)/(1-isqrt2)#

Expression #= (1-isqrt2)/(1+isqrt2) xx (1-isqrt2)/(1-isqrt2)#

#= (1-isqrt2)^2/(1^2-(isqrt2)^2#

#= (1-2sqrt2i+(sqrt2i)^2)/(1^2-(sqrt2i)^2#

Remember: #i^2 =-1#

#:.# Expression #= (1-2sqrt2i-2)/(1-(-2))#

#= (-1-2sqrt2i)/3#

#=-1/3(1+2sqrt2i)#