Question #a05eb

1 Answer
Dec 2, 2017

(a) -2z = 16+(-10)i

(b) #bar z# = -8+(-5)i

(c) #1/z# = #(-8)/sqrt(89)#+#(-5)/sqrt(89) #i

Explanation:

(a) This part is very simple.
You just have to multiply the constant "-2" with the given
expression "z"

so, -2z= -2(-8+5i) = -2(-8) + (-2)(5i)
= 16-10i or 16+(-10)i

(b) In this part we have to find the conjugate of the given expression "z" , its represented by #bar z# .

by conjugate we mean reversing the sign of the imaginary part.

Here the imaginary part is 5i so we replaace it by "-5i".

Therefore #bar z#= -8-5i.

(c) "#1/z#"(reciprocal) means that we have to find the multiplicative inverse of z ,

there's an easy formula for this

#(a/sqrt(a^2+b^2))#+#(-b/sqrt(a^2+b^2))#i

From the question z= -8+5i

Here a= -8 (real part)

b= 5 (from imaginary part)

and #sqrt(a^2+b^2)# = #sqrt89#

Now just plug in the values in the formula , it gives:

#(-8/sqrt(89))#+#(-5/sqrt(89))#i

I hope this helps !
You can tell in the comments , if you have any confusion.