Question

z1 = 2-i, z2=-2+I find Re[z1z2/z1]​

Answer 1

Answer:

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Step-by-step explanation:

Given,

z1 = 2 - i

z2 = i - 2

To find,

Re(z1z2/z1) which means Real part of z1z2/z1.

Procedure,

z1 * z2 = (2 - i)(i - 2) = 2i - 4 - i² - 2i = - 4 - i² = -4 - (-1) = - 4 + 1 = -3

(z1*z2)/z1 = -3/(2-i)

Multiplying and dividing with conjugate of 2 - i which is 2 + i

(z1*z2)/z1 = -3*(2+i)/(2-i)*(2+i)

(z1*z2)/z1 = (- 6 - 3i)/(2² - i²)

(z1*z2)/z1 = (- 6 - 3i)/(4 - (-1)) = (- 6 - 3i)/5

(z1*z2)/z1 = -6/5 - 3i/5

Therefore,

Real part of (z1*z2)/z1 = -6/5