How do you find the power (3-5i)^{4} and express the

Connor Randall

Connor Randall

Answered question

2022-02-02

How do you find the power (35i)4 and express the result in rectangular form?

Answer & Explanation

eris0cg

eris0cg

Beginner2022-02-03Added 13 answers

Step 1
We can use the binomial theorem to expand the expression. (The binomial coefficient from Pascals triangle are 1, 4, 6, 4, 1)
(35i)4=(3)4+4(3)3(5i)+6(3)2(5i)2+4(3)(5i)3+(5i)4
=81+108(5i)+54(25i2)+12(125i3)+(625i4)
=81540i+1350(1)1500(i)+625(1)
=81540i1350+1500i+625
=644+960i

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