Practice 2 Solutions

Evaluate.

$i^{2}$

–1

$i^{78}$

$78 \div 4 = 19 R 2 {(i^{4})}^{19} \cdot i^{2} 1 \cdot - 1$

–1

$i^{15}$

$15 \div 4 = 3 R 3 {(i^{4})}^{3} \cdot i^{3} 1 \cdot - i$

– i

$i^{10}$

$10 \div 4 = 2 R 2 {(i^{4})}^{2} \cdot i^{2} 1 \cdot - 1$

–1

$i^{61}$

$61 \div 4 = 15 R 1 {(i^{4})}^{15} \cdot i 1 \cdot i$

$i^{99}$

$99 \div 4 = 24 R 3 {(i^{4})}^{24} \cdot i^{3} 1 \cdot - i$

– i

Simplify.

$3 \sqrt{- 5} \cdot 2 \sqrt{- 4}$

$3 i \sqrt{5} \cdot 2 i \sqrt{2^{2}} 3 i \sqrt{5} \cdot 4 i 12 i^{2} \sqrt{5}$

$- 12 \sqrt{5}$

$6 \sqrt{- 40}$

$6 i \sqrt{2^{3} \cdot 5}$

$12 i \sqrt{10}$

$\sqrt{- 12} \cdot \sqrt{- 3}$

$i \sqrt{2^{2} \cdot 3} \cdot i \sqrt{3} i^{2} \sqrt{2^{2} \cdot 3^{2}} 6 i^{2}$

–6

$\sqrt{- 196}$

$i \sqrt{14^{2}}$

14i

$20 \sqrt{- 7} \cdot \sqrt{- 14}$

$20 i \sqrt{7} \cdot i \sqrt{2 \cdot 7} 20 i^{2} \sqrt{7^{2} \cdot 2} 140 i^{2} \sqrt{2}$

$- 140 \sqrt{2}$

$\sqrt{- 64}$

$i \sqrt{8^{2}}$

Simplify. Then classify by all sets to which it belongs: real, pure imaginary, complex.

$\sqrt{- 4}$

Pure imaginary, complex

$\sqrt{- 49} \cdot \sqrt{- 100}$

$i \sqrt{49} \cdot i \sqrt{100} 7 i \cdot 10 i 70 i^{2} 70 (- 1) - 70$

Real, complex

$- 5 \sqrt{50} \cdot \sqrt{- 8}$

$(- 5) 5 \sqrt{2} \cdot 2 i \sqrt{2} - 25 \sqrt{2} \cdot 2 i \sqrt{2} - 50 i \sqrt{2^{2}} (- 50 i) (2) - 100 i$

Complex

$\sqrt{- 9} \cdot \sqrt{- 81}$

$3 i \cdot 9 i 27 i^{2} - 27$

Real, complex

$\sqrt{121} - \sqrt{- 20}$

$11 - 2 i \sqrt{5}$

Complex

$\sqrt{- 45}$

$3 i \sqrt{5}$

Pure imaginary, complex