Question

please solve this guy's





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Answer 1

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Given that :-

• |z1| = |z2|
• ARG z1 ~ ARG z2 = π

To show :-

• z1 + z2 = 0

⭐ As we let z1 = x1 + iy1 ,then it will lie in 1st quadrant and given that there is difference of π . So, z2 will lie in the third quadrant as shown in the attachment.

→ Accordingly value of z1 = x1 + iy1

And value of z2 = - x1 - iy1

→ z1 + z2 = x1 + iy1 + ( -x1 - iy1)

→ z1 + z2 = x1 + iy1 - x1 - iy1

→ z1 + z2 = 0