Question

98 POINTS!!!!!!!!!!!!!!!!!!

Answer 1

a = 13

b= 12-5i

Explanation:

Simplify the values and i squared will be -1

Answer 2

a = 13 and b = 12-5i

Explanation:

We need a common denominator

3+2i 5-i

---------- + ---------

3-2i 2+3i

(3+2i) (2+3i) (5-i)(3-2i)

------------------ + --------------------

(3-2i) (2+3i) (2+3i) (3-2i)

Foil the numerators

6 +4i+9i+6i^2 +15-3i-10i+2i^2

------------------ --------------------

(2+3i) (3-2i)

Combine like terms

21 +8i^2

------------------

(2+3i) (3-2i)

We know that i^2 = -1

21 +8(-1)

------------------

(2+3i) (3-2i)

21 -8

------------------

(2+3i) (3-2i)

13

------------------

(2+3i) (3-2i)

Foil the denominator

13

---------------

6 +9i -4i -6i^2

Combine like terms

13

----------------

6+ 5i -6(-1)

13

----------

12 +5i

We know have

13

-------------

12 + 5i

Multiply by the conjugate

13 ( 12-5i)

------------- * -------------

12 + 5i 12 -5i

13 (12-5i)

--------------

144 +25

13(12-5i)

-------------

169

12-5i

------------

13

The parentheses are (12-5i)/13

We need the reciprocal to make the equation become 1

which is 13/ 12-5i

a = 13 and b = 12-5i