Math L3 Module 2

Mathematics NQF Level 3 *see terms and conditions Downloaded from hlayiso.com Mathematics NQF Level 3

Perform operations on complex numbers Module 2 Downloaded from hlayiso.com Mathematics NQF Level 3

Learning activity 2.1 Downloaded from hlayiso.com Mathematics NQF Level 3

1. Simplify the following: 1.6) = 2 + i − 4 − 3i Downloaded from hlayiso.com Learning activity 2.1

Click above to play this video. Downloaded from hlayiso.com Learning activity 2.1

2. Simplify the following and write your answer in rectangular form: 2.6) [ FOIL] (6 − i + 1)(1 + i ) = Rectangular form: z= a + bi Downloaded from hlayiso.com Learning activity 2.1

Learning activity 2.2 Downloaded from hlayiso.com Mathematics NQF Level 3

Simplify the following and write your answer in the a + bi rectangular form: 4) 6 − 2i − 9i + 3i 2 Subsitute i 2 = −1 = 9 − i2 Downloaded from hlayiso.com Learning activity 2.2

Simplify the following and write your answer in the a + bi rectangular form: 4) Continued: Downloaded from hlayiso.com Learning activity 2.2

Learning activity 2.3 Downloaded from hlayiso.com Mathematics NQF Level 3

Learning activity 2.3 Downloaded from hlayiso.com Mathematics NQF Level 3

1. Simplify and write the answer in polar form: 1.3) 2 45°× 8 135° Downloaded from hlayiso.com Learning activity 2.3

2. Simplify and write the answer in polar form: 2.4) Downloaded from hlayiso.com Learning activity 2.3

2. Simplify and write the answer in polar form: 2.6) Downloaded from hlayiso.com Learning activity 2.3

Summative assessment Module 2 Downloaded from hlayiso.com Mathematics NQF Level 3

1. Simplify and write your answer in standard form: 1.1) (4 − 2i ) + ( −6 + 5i ) = 4 − 6 − 2i + 5i =−2 + 3i Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.2) ( 2 + 3i ) (4 − 7i) =8 − 14i + 12i − 21i 2 [ FOIL] =8 − 2i − 21(−1) = 29 − 2i Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.3) Subsitute i 2 = −1 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.4) 2 + i 4 − 3i 2 8 + 6i + 4i + 3i Subsitute i 2 = −1 = 16 − 9i 2 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.4) (Continued) 5 + 10i = 25 1 2 = + i 5 5 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.5) 3 45° + 4 60° 3 [cos 45° + i sin 45°] + 4 [cos 60° + i sin 60°] = 3 [0, 707 + i (0, 707)] + 4 [0,5 + i (0,866)] = 2,121 + 2,121i + 2 + 3, 464i = 4,121 + 5,585i Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.6) Subsitute i 2 = −1 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.6) (Continued) Subsitute i 2 = −1 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.7) Subsitute i 2 = −1 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.7) (Continued) Subsitute i 2 = −1 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.8) Subsitute i 2 = −1 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.8) (Continued) Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.9) 4 − 2i = −6 + 3i + 4i − 2i 2 4 − 2i = Subsitute i 2 = −1 −6 + 3i + 4i − 2(−1) 4 − 2i = −6 + 3i + 4i + 2 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.9) (Continued) 4 − 2i −4 − 7i = =1 −4 + 7i −4 − 7i 4 − 2i −4 − 7i = × −4 + 7i −4 − 7i −16 − 28i + 8i + 14i 2 Subsitute i 2 = −1 = 16 − 49i 2 −16 − 20i + 14(−1) = 65 Downloaded from hlayiso.com Summative assessment – Module 2

1. Simplify and write your answer in standard form: 1.9) (Continued) −30 − 20i = 65 30 20 − − i = 65 65 = −0, 462 − 0,308i Downloaded from hlayiso.com Summative assessment – Module 2

2. Simplify the following complex numbers and leave your answer in polar form: 2.1) 8 cis 60°× 3 cis 40° =(8 × 3) cis (60° + 40°) 24 cis 100° Downloaded from hlayiso.com Summative assessment – Module 2

2. Simplify the following complex numbers and leave your answer in polar form: 2.2) 3 cis 120° × 5 cis 60° 4 cis 30° 3× 5 cis (120° + 60° − 30°) 4 15 cis 150° 4 3, 75 cis 150° Downloaded from hlayiso.com Summative assessment – Module 2

2. Simplify the following complex numbers and leave your answer in polar form: 2.3) 1 180° 2 2 90° × 3 30° 1 = ÷ 6 180° − 90° − 30° 2 Downloaded from hlayiso.com Summative assessment – Module 2

2. Simplify the following complex numbers and leave your answer in polar form: 2.4) Downloaded from hlayiso.com Summative assessment – Module 2

Mathematics NQF Level 2 Downloaded from hlayiso.com Mathematics NQF Level 3