How do you divide 4+2i1−i?

Kinsley Moon

Kinsley Moon

Answered

2022-02-01

How do you divide 4+2i1i?

Answer & Explanation

lorugb

lorugb

Expert

2022-02-02Added 13 answers

You must eliminate the complex number in the denominator by multiplying by its conjugate:
4+2i1i=(4+2i)(1+i)(1i)(1+i)
4+4i+2i+2i21i2
4+6i21+1
2+6i2
1+3i
ocretz56

ocretz56

Expert

2022-02-03Added 16 answers

Require the denominator to be real. To achieve this multiply the numerator and the denominator by the complex conjugate of the denominator.
If (a+bi) is a complex number then (abi) is the conjugate here the conjugate of (1i)is (1+i)
now (4+2i)(1+i)(1i)(1+i)
distribute the brackets to obtain:
4+6i+2i21i2
note that i2=(12)=1
Therefore, 4+6i21+1=2+6i2=22+6i2=1+3i

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