How do you evaluate #(- 1+ 6i ) + ( - 9+ 9i )#?

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Answer 1 · 2017-12-07T15:27:49

#color(blue)(-10+15i)#

We have an expression with two Complex numbers

#color(red)((-1+6i)+(-9+9i))# #color(blue)(Expression.1)#

A Complex number is a combination of a Real Number and an Imaginary Number.

Complex numbers have a standard form: #color(red)a+##color(blue)(bi)#

Where #color(red)a# is the Real Part and #color(blue)(bi)# is the Imaginary Part.

The question involves adding two Complex Numbers in #color(blue)(Expression.1)#

We must now group the Real Part and the Imaginary Part of the Complex Number.

We will use the following Complex Number formula to simplify:

#color(green)((a+bi) +- (c+di) = (a+c)+-(b+-d)i)#

Hence, we can write our #color(blue)(Expression.1)# as

#color(blue)([(-1) + (-9) ]+[ 6 + 9 ]i)#

#color(blue)(-10+15i)# our final answer

I hope this helps.