How do you simplify (8+6i)−(2+3i)?

1 Answer
Andre R.
Oct 23, 2016

3⋅√5⋅(cos(0.464)+isin(0.464))

Explanation:

First simplify Cartesian form,
(8+6i)−(2+3i)=8−2+6i−3i
=6+3i

now to convert to trigonometric form,

6+3i=r⋅cis(θ)

where,
r=√62+32
r=√45 (which can be further simplified to 3⋅√5)

and,

θ=tan−1(36)

θ=0.464 (3dp, radians)

so we can express (8+6i)−(2+3i) as,

3⋅√5⋅cis(0.464)

or in expanded version,
3⋅√5⋅(cos(0.464)+isin(0.464))

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