Question

The modulus of (1 + 2i)^4 is _____.
5
20
25
625

Answer 1

`|z|=25`

Explanation:

The given expression is:

`(1+2i)^4`

The exponent is not very large so we can expand it.

`(1+2i)^4=(1+2i)^2(1+2i)^2`

`(1+2i)^4=(4i-3)(4i-3)`

`(1+2i)^4=16i^2-12i-12i+9`

`(1+2i)^4=-16-12i-12i+9`

`(1+2i)^4=-7-24i`

The modulus is

`|z|=√((-7)^2+(-24)^2)`

`|z|=√(49+576)`

`|z|=√(625)`

`|z|=25`