Answer Key 9.9
- 3+8−4i3+8−4i
11−4i11−4i - 3i−7i3i−7i
−4i−4i - 7i−3+2i7i−3+2i
9i−39i−3 - 5−6−6i5−6−6i
−1−6i−1−6i - −6i−3−7i−6i−3−7i
−13i−3−13i−3 - −8i−7i−5+3i−8i−7i−5+3i
−12i−5−12i−5 - 3−3i−7−8i3−3i−7−8i
−4−11i−4−11i - −4−i+1−5i−4−i+1−5i
−3−6i−3−6i - i−2−3i−6i−2−3i−6
−2i−8−2i−8 - 5−4i+8−4i5−4i+8−4i
13−8i13−8i - −48i2−48i2
−48(−1)−48(−1)
4848 - −24i2−24i2
−24(−1)−24(−1)
2424 - −40i2−40i2
−40(−1)−40(−1)
4040 - −32i2−32i2
−32(−1)−32(−1)
3232 - 49i249i2
49(−1)49(−1)
−49−49 - −7i2(4−3i)−7i2(4−3i)
−28i2+21i3−28i2+21i3
−28(−1)+21(−1)i−28(−1)+21(−1)i
28−21i28−21i - 36+60i+25i236+60i+25i2
36+60i+25(−1)36+60i+25(−1)
36+60i−2536+60i−25
11+60i11+60i - 16i2(−2−8i)16i2(−2−8i)
32i2+128i332i2+128i3
32(−1)+128(−1)i32(−1)+128(−1)i
−32−128i−32−128i
- aa
56−42i+32i−24i256−10i−24(−1)+24⟸80−10i56−42i+32i−24i256−10i−24(−1)+24⟸80−10i - 9i2(4−4i)9i2(4−4i)
−36i2+36i3−36i2+36i3
−36(−1)+36(−1)i−36(−1)+36(−1)i
36−36i36−36i - aa
−8+10i+28i−35i2−8+38i−35(−1)+35⟸27+38i−8+10i+28i−35i2−8+38i−35(−1)+35⟸27+38i - −32i+64i+4+12i−32i+64i+4+12i
−28+76i−28+76i - aa
32+24i−16i−12i232+8i−12(−1)+12⟸44+8i32+24i−16i−12i232+8i−12(−1)+12⟸44+8i - −18i+12i2−28i2−18i+12i2−28i2
−18i+12(−1)−28(−1)−18i+12(−1)−28(−1)
−18i−12+28−18i−12+28
−18i+16−18i+16 - aa
2+10i+i+5i22+11i+5(−1)−5⟸−3+11i2+10i+i+5i22+11i+5(−1)−5⟸−3+11i - aa
−6+3i+10i−5i2−6+13i−5(−1)+5⟸−1+13i−6+3i+10i−5i2−6+13i−5(−1)+5⟸−1+13i - −9+5ii⋅ii⇒−9i+5i2i2⇒−9i+5(−1)(−1)⇒9i+5−9+5ii⋅ii⇒−9i+5i2i2⇒−9i+5(−1)(−1)⇒9i+5
- −3+2i−3i⋅ii⇒−3i+2i2−3i2⇒−3i+2(−1)−3(−1)⇒−3i−23−3+2i−3i⋅ii⇒−3i+2i2−3i2⇒−3i+2(−1)−3(−1)⇒−3i−23
- −10i−9i6i⋅ii⇒−10i−9i26i2⇒−10i−9(−1)6(−1)⇒−10i+9−6−10i−9i6i⋅ii⇒−10i−9i26i2⇒−10i−9(−1)6(−1)⇒−10i+9−6
- −4+2i3i⋅ii⇒−4i+2i23i2⇒−4i+2(−1)3(−1)⇒−4i−2−3−4+2i3i⋅ii⇒−4i+2i23i2⇒−4i+2(−1)3(−1)⇒−4i−2−3
- −3−6i4i⋅ii⇒−3i−6i24i2⇒−3i−6(−1)4(−1)⇒−3i+64−3−6i4i⋅ii⇒−3i−6i24i2⇒−3i−6(−1)4(−1)⇒−3i+64
- −5+9i9i⋅ii⇒−5i+9i29i2⇒−5i+9(−1)9(−1)⇒−5i−9−9⇒5i+99
- 10−i−i⋅ii⇒10i−i2−i2⇒10i−(−1)−(−1)⇒10i+1
- 105i⋅ii⇒10i5i2⇒10i5(−1)⇒10i÷−5−5÷−5⇒−2i
- 4i−10+i⋅−10−i−10−i⇒−40i−4i2(−10)2−(i)2⇒−40i−4(−1)100−−1⇒−40i+4101
- 9i1−5i⋅1+5i1+5i⇒9i+45i2(1)2−(5i)2⇒9i+45(−1)1−25i2⇒9i−451−25(−1)⇒9i−451+25⇒
9i−4526 - 87−6i⋅7+6i7+6i⇒56+48i72−36i2⇒56+48i49−36(−1)⇒56+48i49+36⇒56+48i85
- 44+6i⋅4−6i4−6i⇒16−24i16−36i2⇒16−24i16+36⇒(16−24i)÷452÷4⇒4−6i13
- 710−7i⋅10+7i10+7i⇒70+49i100−49i2⇒70+49i100+49⇒70+49i149
- 9−8−6i⋅−8+6i−8+6i⇒−72+54i64−36i2⇒−72+54i64+36⇒(−72+54i)÷2100÷2⇒
−36+27i50 - 5i−6−i⋅−6+i−6+i⇒−30i+5i236−i2⇒−30i−536+1⇒−30i−537
- 8i6−7i⋅6+7i6+7i⇒48i+56i236−49i2⇒48i−5636+49⇒48i−5685
- ±9i
- √−5⋅9⇒±3√5i
- √−20⇒√−4⋅5⇒±2√5i
- √24⇒√4⋅6⇒±2√6
- 3+√3⋅−96⇒3+3√3i6⇒1+√3i2
- −4−√−2⋅4−4⇒−4−2√2i−4⇒2+√2i2
- 8−4i4⇒2−i
- 6+√2⋅−164⇒6+4√2i4⇒3+2√2i2
- i
- i3⇒−i
- 1
- 1
- i2⇒−1
- i
- i2⇒−1
- i3⇒−i