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

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Answer 1 · 2017-12-07T15:27:49

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

We have an expression with two Complex numbers

$(- 1 + 6 i) + (- 9 + 9 i)$ $color(red)((-1+6i)+(-9+9i))$ $E x p r e s s i o n .1$ $color(blue)(Expression.1)$

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

Complex numbers have a standard form: $a +$ $color(red)a+$ $b i$ $color(blue)(bi)$

Where $a$ $color(red)a$ is the Real Part and $b i$ $color(blue)(bi)$ is the Imaginary Part.

The question involves adding two Complex Numbers in $E x p r e s s i o n .1$ $color(blue)(Expression.1)$

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:

$(a + b i) \pm (c + d i) = (a + c) \pm (b \pm d) i$ $color(green)((a+bi) +- (c+di) = (a+c)+-(b+-d)i)$

Hence, we can write our $E x p r e s s i o n .1$ $color(blue)(Expression.1)$ as

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

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

I hope this helps.

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