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

As we know that,i = √(-1 ), i2 = -1, i3 = -i, i4 = 1z = in + in+1 + in+2 + in+3= in (1+i1+i2+i3 )= in (1+i-1-i)= in(0)= 0

Q21 of 153 Page 14

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

As we know that,

i = √(-1 ), i² = -1, i³ = -i, i⁴ = 1

z = iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³

= iⁿ (1+i¹+i²+i³ )

= iⁿ (1+i-1-i)

= iⁿ(0)

= 0

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.

Write the conjugate of.

Find the real value of a for which 3i³ – 3ai² + (1 – a) i + 5 is real.

If |z| = 2 and find z.