Worksheet #19: Complex Numbers | Highline College - Edubirdie

University:
Highline College
Course:
MATHP 141 | Precalculus I Plus Extra Support
Academic year:

2022
Views:

99

Pages:

1
Author:

texans105bvn

Workshop #19 1. Let the letter i have the property that i2 = −1. (a) Compute the following i i2 i3 i4 = = = = i −1 i5 i6 i7 i8 i9 = = = = i10 i11 i12 = = = = (b) What pattern do you notice? (c) Use this pattern to compute i21 i102 i616 i3273 2. Add or subtract and combine like terms (a) (2 + 4x) + (1 − 3x) (c) (2 + 3x) − (1 + 3x) (b) (2 + 4i) + (1 − 3i) (d) (2 + 3i) − (1 + 3i) 3. Multiply out the following 1 (2 − 4x) 2 1 (b) (2 − 4i) 2 (a) x (5 − 3x) 2 i (d) (5 − 3i) 2 (c) (e) (1 + x)(2 − 3x) (f) (1 + i)(2 − 3i) 4. Multiply the following (a) (2 + 3i)2 (b) (2 + 3i)(2 − 3i) √ √ (c) ( 3 − i)( 3 + i) √ √ √ √ (d) ( 2 + 3i)( 2 − 3i) (e) (a + 2i)(a − 2i) (f) (a + bi)(a − bi) 5. Use your answer from part f of the previous problem to ﬁnd real numbers a and b such that (2 + 3i)(a + bi) = 13. Adjust your previous answer to ﬁnd real numbers c and d such that (2 + 3i)(c + di) = 1.

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