Question

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

Answer 1

Answer:

$|z|=25$

Step-by-step 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

$|z|=\sqrt{(-7)^2+(-24)^2}$

$|z|=\sqrt{49+576}$

$|z|=\sqrt{625}$

$|z|=25$