No. of nonzero terms in ${\left(1+x\right)}^{42}+{\left(1-x\right)}^{42}+{\left(1+ix\right)}^{42}+{\left(1-ix\right)}^{42}$  is

$2\left({}^{42}{C}_0+{}^{42}{C}_2{x}^2+\cdots +{}^{42}{C}_{42}{x}^{42}\right)\text{21 terms}$

$+2\left({}^{42}{C}_0+{}^{42}{C}_2{\left(ix\right)}^2+\cdots \right)\text{21 terms}$

No. of terms are $\left[\frac{n+4}{4}\right]=\left(\frac{42+4}{4}\right)=\frac{46}{4}=11$

11 terms.