How do I find the quotient of two complex numbers

iocasq4

iocasq4

Answered question

2022-02-01

How do I find the quotient of two complex numbers in standard form?

Answer & Explanation

Appohhl

Appohhl

Beginner2022-02-02Added 11 answers

Step 1
Let z1=a1+b1i and z2=a2+b2i. We want to find
q=z1z2=a1+b1ia2+b2i
Generally, we wish to write this in the form
q=A+Bi
Where A and B are real numbers. To do this, we must amplify the quotient by the conjugate of the denominator:
q=z1z2×z2z2
=a1+b1ia2+b2i×a2b2ia2b2i
=(a1a2+b1b2)+(b1a2(b1a2b2a1)i}{a22+b22}
q=a1a2+b1b2a22+b22+b1a2b2a1a22+b22i

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