The variable z is often used to denote a complex number and z¯ is used to denote its conjugate. If z = a+bi, simplify the expression z^{2}-\overline{z

emancipezN

emancipezN

Answered question

2021-07-02

The variable z is often used to denote a complex number and z¯ is used to denote its conjugate. If z=a+bi, simplify the expression
z2z2

Answer & Explanation

Benedict

Benedict

Skilled2021-07-03Added 108 answers

With z=a+bi, the conjugate, z, is a-bi. Hence, the expression z2z2, is equivalent to
(a+bi)2(abi)2=[(a)2+2(a)(bi)2][(a)22(a)(bi)+(bi)2]
(use(a+b)2=(a)2+2(a)(b)+(b)2)
=[a2+2abi+b2i2][a22abi+b2i2]=a2+2abi+b2i2a2+2abib2i2=(a2a2)+(2abi+2abi)+(b2i2b2i2)=0+4abi+0=(4abi)i.
Hence, z2z2=(4abi)i.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?