Mark the correct answer for 3 i^ 34 +5 i^ 27 -2 i^ 38 +5 i^ 41 = … - Vidyadip

MCQ

Mark the correct answer for $3 i^{34}+5 i^{27}-2 i^{38}+5 i^{41}=$ ?

A
$1$
✓
$-1$
C
$-4i$
D
$10i$

✓

Answer

Correct option: B.

$-1$

$3^{34}+5 i^{27}-2 i^{38}+5 i^{41}$
$=3 \times\left(i^4\right)^8 \times i^2+5 \times\left(i^4\right)^6 \times i^3-2 \times\left(i^4\right)^9 \times i^2+5 \times\left(i^4\right)^{10} \times i$
$=3 \times 1 \times(-1)+5 \times 1 \times(-i)-2 \times 1 \times(-1)+5 \times 1 \times i$
$=-3-5 i+2+5 i$
$=-1$

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