for any two complex numbers z1 and z2 and any two real numbers a, b find the value of |az1 – bz2|2 + |az2 + bz1|2.

|az1-bz2|2 + |az2+bz1|2= | z1|2 (a2+b2 )+| z2|2 (a2+b2 )= (a2+b2 )(| z1|2+| z2|2)

Q19 of 153 Page 14

for any two complex numbers z₁ and z₂ and any two real numbers a, b find the value of |az₁ – bz₂|² + |az₂ + bz₁|².

|az₁-bz₂|² + |az₂+bz₁|²

= | z₁|² (a²+b² )+| z₂|² (a²+b² )

= (a²+b² )(| z₁|²+| z₂|²)

Write the value of

If |z + 4| ≤ 3, then find the greatest and least values of |z + 1|.

Write the conjugate of.

If n ∈ N, then find the value of iⁿ + i^{n + 1} + i^{n + 2} + i^{n + 3}.