How do you simplify [2(cos⁡(7π4)+isin⁡(7π4))]÷[22(cos⁡(3π4)+isin⁡(3π4))] and express the result in rectangular form?

Jay Mckay

Jay Mckay

Answered

2022-02-01

How do you simplify [2(cos(7π4)+isin(7π4))]÷[22(cos(3π4)+isin(3π4))]
and express the result in rectangular form?

Answer & Explanation

fumanchuecf

fumanchuecf

Expert

2022-02-02Added 21 answers

Step 1
2(cos(7π4)+isin(7π4))22(cos(3π)+isin(3π4))
=2(cos(7π4)+isin(7π4))(cos(3π4)+isin(3π4))
Step 2
=2ei7π4ei3π4
=2ei(7π43π4)
=2eiπ
=2(cosπ+isinπ)
=2(1+i0)=2+i0
tainiaadjouctlw

tainiaadjouctlw

Expert

2022-02-03Added 14 answers

Two divide two complex numbers, we divide their moduli and subtract their arguments.
So our number will have modulus
222=112=2
and argument of
74π34π=44π=π
So our number will be
2(cosπ+isinπ)=2(1+0i)=2+0i

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